I believe that local and national FIRST.ORGs have decent records of FTC events along with FRC events (These records however, do not contain some of the collective information about team records over the years or their annual average or total records). I have no clue whatsoever about VEX records. FLL... nearly 20,000 teams and four scores for each... not including the awards and multiple tiers of competition... bad idea from an information logistics standpoint.
If there are central FTC and VEX equivelants to The Blue Alliance it would be a wonderful discovery to this community!
{For those thinking it: Is it not hard enough for these guys (The Blue Alliance) to program for and keep track of 2070 FRC teams, let alone another 1500 FTC teams, and who knows how many other VEX teams!? TBA please stay the way you are (Perfect!) and dont worry about FTC and VEX... let someone else worry about those!
}