How often slop affects the outcome depends on various things, but if the race is long enough,
it's not enough to change the outcome of the match (over the long run, on average, most of the time, etc.)
"Long enough" means both players get several trips to the table with an opportunity to control their destiny.
In the APA, 20+ innings is very common. I'd say that's long enough.
Everyone has their bad beat story about the lucky APA 1, I have it too.
Just like that guy who had a 98% winning hand in poker then lost.
But with 20+ opportunities, it's usually not luck that decided the match.
Handicapping on the other hand... can be as extreme as you want it to be.
There's no limit to how heavy the handicap can be. 95 balls in a race to 100 for example.
I think most handicapping is designed to turn every match into a 50/50 coin flip.
Therefore any player crying that they're getting screwed by the handicapping,
better have well under 50% win rate. If they're winning significantly more than that...
the handicapping is not strong enough and the high-rank player is getting the best of it.
Anyway to answer your question, it depends on how you define "Better" or "more fair".
"Better" = most fun for all players? Handicapped, without a handicap the weakest players lose a lot and quit.
"Better" = the best players win the most? Then slop. Without handicaps, the best player wins almost every match.
"More fair" = everyone can win? Like each match is a coin flip? Then handicapped.
"More fair" = the guy who has more skill should always win? Then allow slop and no handicaps.