I'm for variation and character being locked for the winner. Here are some reasons.
1. Loser should be allowed to effectively counter-pick. We all know that fighting games are not 100% balanced, and because of that, somebody is always at some sort of advantage (unless it's a mirror match). The loser should be allowed to select either a new character or new variation without fear that his counter-pick won't be countered with another disadvantageous match-up.
2. Simplicity. If you let both players choose variations (even blind) after each game, you will have a long character selection process between each game where both players are debating which variation the other will choose, which will influence their choice.
3. It promotes character/variation variety. If you know that you can effectively counter-pick without the opponent having some sort of answer for your counter, you are more likely to do it. If you know that the opponent could counter your pick, you are less likely to change and more likely to 'stick to your guns'.
This is basically the safest, least complicated rule set to start with. Starting with all kinds of crazy rules can cause issues, as it did with Injustice.