I've found that it makes a big difference. My best players range from average to proficient in stamina and the strong/proficient guys can play big minutes at a high level, assuming their game shape is also solid. I would warn you that guys with high stamina tend to play more minutes so you have to monitor those minutes in order to make sure they maintain a high level of game shape. I've been training stamina twice per season but this season am only doing it once as my key guys are already at a good level.
I wish there were pigmen. You get a few of these pigmen walking around I'm looking a whole lot better. Then if somebody wants to fix me up at least they could say, Hey he's no pig-man!