multum in parvo
Even though Shadow has one of the more developed backstories in Final Fantasy VI, he very rarely speaks or interacts with the other characters, which leads one to think -- does he even have a personality? Well of course he does, but like his backstory, it's subtle. His defining characteristics aren't as easy to pinpoint as Edgar's, for example, but with a little digging, they can be found. And ultimately, I think this subtlety in itself says a great deal about who he is.
While I hate to say that Shadow's personality is riddled with self-doubt, I would be crazy not to mention it. Based on his occupation, you would think he would be pretty confidant -- successful thieves and assassins tend to brag about their exploits, but Shadow is noticeably quite on the topic. In fact, Shadow is never the one who tells the party about his reputation -- Edgar and various town citizens inform the party of how hardcore Shadow is. To Shadow, the work he does is nothing worth bragging about, and he unlike the majority people in his line of work, he seems passively resigned to it.
There is one scene in particular that showcases to what extent Shadow experiences self-doubt, and it is right after the party battles the Atma Weapon on the Floating Continent. Shadow tells the party that he has no right to fight with them because he worked for the Empire, and he takes off. He does not feel that he is worthy enough to be fighting along side a group with such a noble cause, but he fails to see that he is not the only one with connections to the Empire -- both Terra and Celes did far more damage working for the Empire than he ever did. Nevertheless, he sticks around long enough to see the party endangered by Kefka, and he saves them by distracting Kefka and risking his own life in the process. This selfless act is never mentioned by him after the fact, and it's pretty clear that he fails to recognize how heroic feat it was. The irony, of course, is that this act more than proved his worth, but he still fails to see it.
Some people are outgoing, and others like to keep to themselves. Shadow definitely prefers to keep to himself. If you see Shadow sitting along in a cafe, chances are that he'll tell your party to leave him alone or to go away. He is not there to make friends -- he is more or less lost in his own thoughts, his only distraction being Interceptor. Even once he does decide to join your party, he very rarely chooses to interact with anyone. He is never involved in important decisions, and he decides to go with the flow if it just so happens to suit him. He even makes the decision to depart for good on his own -- while the rest of the party is helping each other escape Kefka's tower safely, Shadow slips out on his own, only telling Interceptor of his decision to leave. It is unclear where he was going and why he was going there, but that just highlights his introverted nature -- all that mattered was that he knew, and he saw no need to inform the party of his whereabouts.
I don't know that the average person would describe Shadow as a compassionate man, but I think he is in a subtle way. He claims that he only cares about making money and supporting his dog, but somehow he is always near when the party needs him the most. He does not interact much with the people in the party, but he does not see that as being his duty -- he himself states that the only thing he knows how to do is fight, so by lending them his power, he is able support them without doing so verbally. He saves the day more than once -- both in the burning house and on the Floating Continent -- and while he makes excuses for his heroic behavior, it is clear that he was genuinely concerned. Shadow may not be a master with words, but he seems to realize that actions go much further, anyway.