There's a fair bit of variety in the different masters, as a lot are dual faction so can hire some interesting choices from their 'other' faction. Their styles are also quite different; Shenlong and McCabe are force multipliers in that they can get more from their crews, Misaki is a fragile but deadly assassin, Lynch and Mei are both good damage dealers, Yan Lo and Asami can summon in two different ways, and Brewmaster I don't know much about but think he works mainly around locking down the enemy.
Personally I play Shenlong mainly as I find I can do most schemes etc with his crew, although I also have Lynch for when I just want to kill things, and Mei for when lots of stuff is likely to be bunched up in one place.
Some of the main advantages I find are that Thunders have access to quite a lot of ways to get focus and fast, as well as some useful pushes, which I find makes them quite mobile compared to some other factions. Also they have Ten Thunders Brothers who are excellent for 5ss! An advantage all to themselves