One of the issues with categorizing BattleTech heroes is that different authors take very different approaches to the universe - almost to the point that some stories seem to be of different genres.
Michael Stackpole has one of the most recognizable styles - pure two-fisted pulp hero action, with strong-jawed invincible heroes who always save the day and get the girl, where the evil foemen are revealed as being both immoral and stupid, and more often than not are hoist by their own petard en route to getting annihilated by the bare-knuckled awesomeness of the heroes. It's not genetics, so much, as it is the style of the "pulp" approach. The heroes' only flaw is that they are too modest to fully realize how awesome they are, and often feel crippled by worry about the impact of their actions on others...because they've got heart, y'know?
By contrast, Ilsa Bick's heroes are tormented souls because they've seen too much, stared into the abyss and seen it wink back, and have some serious kinks upstairs that drive them to do what they do. Her protagonists are often a great distance from the norms of the BattleTech universe.
Robert Charrette's heroes tend to be more deeply realized (by comparison to Stackpole's), with lots of secrets in their backstories, conflicts between duty, honor, and loyalty, and plans for the future. Not everything they try works, but you get the sense that they're parts of a larger organization (and that those organizations are full of internal power loci competing for influence, and that the organizations themselves are locked in conflict with each other), and that they have resources they can fall back on. They're team players, while Stackpole's heroes are mainly lone wolf superheroes (look at Xiang, for instance).
William Keith primarily focused on Grayson Carlyle and his descendants. His heroes are often defined by their ability to keep going in the face of massive losses. In nearly every engagement, the Legion and its allies take heavy casualties. Grayson leaves a trail of bodies (his own side's) as they carry on their campaign. They've had their headquarters overrun at least four times (counting the loss of the Citadel on Trell I by Carlyle's Commandos). Grayson leads his troops into an ambush on Trell I and gets arrested, then is only able to muster a half-hearted inspirational speech to the survivors up at Thunder Rift, but still soldiers on even though hope seems lost. The whole cadre mission on Verthandi goes belly up almost immediately, and he still manages to rally back and rebuild the resistance. The Legion lost their landhold and transports, and were branded criminals on Helm. They lost Glengarry to Free Skye. The monorail disaster on Hesperus shattered the command. And yet they persisted.
Stackpole's Kell Hounds, in Grayson's place, would have never lost the fort on Trell I in the first place, and would have punched their way through the Combine commandos (probably pre-warned about the traitor by an attractive Heimdall plant in their ranks), and they would have one-shotted the Oberon lance when it dared to show its face.
Vic Milan's heroes tend to have tragic backstories and be somewhat driven by the resultant psychological damage (though, in some cases, they're sidelined by the psychological damage, giving room for the lower ranking protagonists to rise up and take a leadership role). In many cases, they're trying to get revenge for past wrongs, or trying to atone for past misdeeds/failings.
Edward Smith's lone hero stands out as fumbling towards heroism on the sole basis of being a massive idiot. (Johnny Mace, 'Mech Ace, is essentially Cartoon Network's "Johnny Bravo" as a MechWarrior.)
Jason Schmetzer's heroes have, I think, the widest range of any of the authors, probably since he's done mostly short stories (in addition to being the Track master). They're idealistic - willing to fight and die for what's right. They're burnt out and emotionally dead inside from putting their unparalleled skill at killing to work. They're doing penance for having displayed cowardice in the face of the enemy. They're fighting against impossible odds to protect their fellow troops, who they see as family. They've suffered massive betrayal and personal losses, and they're fighting for vengeance. They're fighting to put another notch on their belts and boost their reputation. They're entitled nobles who view the lesser folk as cannon fodder, and care only about their own reputations and cash flow. They're people who have seen their dreams snatched away, and are having to adapt to their new reality.