My son played in the Baseball Youth All-American games in Indiana this summer and was invited to the "Best of the Best" tournament you mentioned.
I will say this: he had a blast. He completely loved it. The competition was pretty good, not consistently great, but pretty good. My son was 13U and the 13U/14U age groups were combined, so that was good in terms of "playing up" for my kid. The competition was several levels down from what I saw on the Perfect Game 14U Showcase field, but there were some good players there. We kept expenses down by driving there and treating it more as as part of a family vacation (had been wanting to go to the Indiana Dunes on Lake Michigan for years).
There weren't any "scouts" there, nor was I expecting any. Certainly not any college scouts. We won't be going to the Vero Beach event, mostly because it is during the time we are making our son take time off, but also just the expense of flying cross country.
Baseball Youth puts on good events. My son would love to go back next year, we'll weigh our options. If we do go it'll be purely for the fun of it, not with any expectations of it furthering anything more than the love for the game (which is a reward in itself)