It is more depend on your play style. The more you enjoy a certain playstyle, the easier it is for the commander that fits that kind of playstyle.
You want the least amount of effort? P1 Stukov. Spam Diamond back and your good to go, no micro or macro needed and at the same time clears an area in mere seconds.
P2 Karax: You can finally build the units you want to and mess around
P1 Raynor: Now all the annoying macro is gone when you want a casual and enjoyable non Death Grinder game living the dreams of a non 100000 casualty Raynor DeathCamp. 99% of surviving not dead marines agree, being Alive is great!
P3 Tychus: Honestly really doesn’t really change the gameplay much despite dropping a odin. At worst you lose your nuke but get a Robot and trade Medivac Mastery for more Robot. But you hardly ever used the Tychus Caging Odin before unless you had a base to nuke. So outside of Void Thrasher It’s a pretty decent all rounder. It actually has some accidental tanking synergy with Vega MC builds as well too, previously all mcs seemed to have a dramatically higher aggro than your outlaws, nearly instantly being ripped to shreds on their 0 armor. Now with Dogwalker the Odin draws a lot of threat and helps compensate for the low base dps of mc builds (while also facetanking), allowing you to extract mind controled units easier and be able to mess around with greedy plays or builds. (2/4 Tychus, 1/4 Rattlesnake, 0-1/4 Sam, 1-2/4 to 4/4 Vega, 2/4 Nikara) And go crazy on Carriers/Thors/Bcs/Science Vessels / Arbiters / Collossi. (Skip zerg though for the most part, not really much good besides Brood lords and 0 armor ultralisks get eaten in seconds by +3/3 zerglings. )