The short answer to what might appear a trick question is--well--it depends. On this topic, ironies and paradoxes abound. Whereas "big and strong" are words frequently used to complement each other, so-called big egos are actually diametrically opposed to strong ones. It's something like, "The bigger they are, the harder they fall." Or, simply put, contrasted with big egos, strong egos can take a fall much better. With more balance, resilience and personal power, when they take a hit they're much better in getting back up.
To expand on this distinction, people with strong egos can be viewed generally as self-confident; secure and emotionally stable; flexible, adaptive, and able to cope well with everyday stresses and frustrations; mature, independent, and resourceful; and authentic. On the contrary, those with big egos lack inner stability and are more easily upset; tend to be rigid, reactive, dogmatic, and egocentric; simulate self-confidence (rather than truly possess it); display arrogance and a narcissistic sense of entitlement; show deficits in personal integrity; and, perhaps more telling than anything else, demonstrate--when feeling threatened--a surprising weakness, even fragility. Although such egos may, indeed, be "oversized," their actual bigness or stature has largely to do with ego-inflation, vs. any real ego strength.
Without much concrete substance, the grandiosity, or bravado, inherent in big egos might be compared to a balloon--filled to capacity (and with hot air, at that!) and ready to burst (i.e., suddenly and completely deflate) at the slightest prick. Similarly, the superficially positive sense of self that typically characterizes people with big egos is quite vulnerable. Because their self-esteem is not firmly anchored from within, to stay propped up it requires constant external support. When that support is missing, or withdrawn, such individuals can experience anxiety or depression. Much more likely, however, they'll react with anger--so as instantaneously to invalidate whoever, or whatever, is felt to be invalidating them. By employing this (mostly unconscious) defense, they may restore a positive sense of self far too easily punctured by external circumstances.
All of which is to say, paradoxically, that the bigger the ego, the weaker the ego. People who are self-centered and "full" of themselves are driven by an ego that, essentially, is "anemic." They're compelled to act--and react--in conjunction with a whole host of potent psychological defenses designed to safeguard their unstable sense of self. Their personal insecurities may in fact be so well masked that they're hidden not only from others, but also from themselves. Whatever emotional fortitude they possess hinges on how well their defenses operate to ward off external threats. Lacking the resources to tolerate feelings of vulnerability (i.e., be able to confront reality as it is--free of defenses), they stubbornly resist negative feedback or criticism.
Contrast this with people who've developed truly strong egos. Nowhere as self-involved-or as cocky, prideful, narcissistic, or even (dare we use the word?) "egomaniacal"--people with strong egos genuinely believe in themselves. Therefore they don't require anything like the acknowledgment or recognition that those with big egos must depend upon. Far more likely to be givers than takers, and to support others rather than demand support from them, they reveal an openness and trust barely perceptible in those with big egos.
Additionally, people with big egos are governed by their neediness. With so many of their behaviors literally dictated to them by their defenses, they can't focus their attention on others the way those with stronger egos (or perhaps we should say, more evolved egos) are able to. Lacking the flexibility that emanates from ego strength, their personalities reflect a broad-based rigidity. They'll obstinately cling to their point of view and be unable to grasp, or accept, those of others. Unable to understand or be compassionate to people they disagree with, their overall attitude is likely to be both critical and dismissive. To suspend their own way of seeing things and identify with another's viewpoint feels somehow compromising to them, so that--in their protective self-righteousness--they can be frustratingly tone-deaf in appreciating where others are coming from.
In opposition to this, people with strong egos demonstrate not only the flexibility to appreciate and validate viewpoints other than their own, but to accommodate and integrate them as well. They're able to do so because others' viewpoints aren't personally threatening to them. And beyond not feeling invalidated by people who don't share their ideas, they may even solicit divergent points of view in order to become better informed about something. Secure in the legitimacy of their own thoughts and feelings, they're not driven from deep within to avoid, resist or deny another's. It's as though people with strong egos live their lives in expansive mode, whereas people with big egos--feeling so obliged to erect protective safeguards for themselves--are doomed to go through life controlled by all sorts of self-imposed constrictions and constraints.
Moreover, people with big egos--because they're continually compelled to aggrandize their essentially impoverished selves--can be markedly insensitive (or even blind) to what's going on inside others. Strong egos, on the other hand, have both the ability and inclination to direct their attention outside themselves. More confident, and so nowhere as defensive as those with big egos, they're far more likely to understand, and sympathize with, the experiences of others--especially those unlike themselves.
And their empathy, far more developed, is also considerably more accurate. Not regarding themselves as in competition with others, they don't feel compelled (as a way of propping up their self-esteem) to disparage or de-value them. And without the perceptual barriers that result from donning self-protective armor, they're far better equipped to see others as they really are, vs. a projection of their own defense-ridden egos. For example, when people with strong egos get a negative reaction from others, they're far less likely (than those with big egos) to rationalize that these others are jealous of, or threatened by them.
Similarly, people with strong egos don't always have to be right, and can readily admit when they're wrong. This is hardly the case with big egos, who strive--at times, desperately--to get in the last word. Constantly needing to prove themselves, it's difficult for them to let something go, or to put the welfare of a relationship before their own immediate need to feel right and superior. Even when they are obliged to admit errors or accept blame, they're likely to emphasize that, after all, everybody makes mistakes. Or they'll qualify their admissions ad nauseam (i.e., such that they seem almost to be relinquishing responsibility for any wrongdoing). Or, finally, they'll do all they can to minimize their mistakes--even as, presumably, they're owning up to them. It's as though the cost to their basically frail ego of being found to be less than perfect simply feels too exorbitant. And so they're driven, at almost every turn, to "tone down" their admissions.
Just as big egos try to make light of their failures--and may have an incredibly difficult time apologizing or saying "I'm sorry"--they're also inclined to accentuate or exaggerate their successes. And, as opposed to those with strong egos (who are generally happy to share credit for their achievements), it's hard for them to resist the temptation to take full credit for accomplishments they may not be wholly responsible for--tending to play down any help they've received from others. Worse than this, they tend to take credit for things they've played only the most inconsequential role in bringing about. Unconsciously, almost desperate to compensate (or better, over-compensate) for a deep sense of limitation or deficit, they're "expert" at plagiaristically passing off others' ideas, words or deeds as their own.
In short, the many unflattering descriptions of people with big egos enumerated above all signify their need to make up for a fundamental lack of true self-esteem. I employ the word "true" here advisedly, for people with big egos are able to feign a certain positive (if not overblown) self-regard--though, to be sure, it's highly fragile and requires tremendous defensive energy to hold together. The defenses themselves are predominantly narcissistic, reflecting a self-love less real or heartfelt than contrived and conditional. Most of the negative characteristics of people with big egos, therefore, indirectly provide insight into their acutely felt weaknesses or shortcomings--frailties they're forever struggling to disguise (and at least as much from themselves as anybody else).
If, finally, our egos can best be viewed as the image we hold of ourselves, then if we have a big ego we're viewing ourselves self-delusively, according to an ideal that goes beyond our actual reality. In such cases, it's clear that our ego--before it can even begin to be developed anew--is in need of significant "shrinking." If, on the other hand, our ego is weak not because we're self-aggrandizing but because we're excessively self-critical, then the best way for us to strengthen it is to view ourselves with greater kindness, understanding and compassion. Additionally, we may need to learn how to overcome our various anxieties and begin more effectively to confront life's many challenges. Only then--as a result of correcting our habitually negative self-talk and coping more successfully with common, everyday obstacles--can we experience a genuinely positive sense of self, one that is as strong and stable as it is reality-based.
In the end, a strong ego is indistinguishable from a healthy one. Learning how to feel good about ourselves as we are, and beginning to better appreciate our strengths (as well as make peace with our weaknesses), is the ideal way of "growing" our ego to precisely the right size and strength. And that task, should we choose to undertake it, isn't just ours--it's everyone's.