Just to clarify from the start, I'm not actually arguing that they are equally strong prospects. Also, as fair warning, this is a fantasy-related question.
I'm in a deep dynasty league with fairly regular scoring where I will almost certainly not have the choice between them, but I was thinking about who I would choose if for some reasons, they fell down to my spot in the draft. According to the most favorable projections, Beckham could be a .290 hitting SS with average power and maybe 30 SB speed - in other words, maybe a Derek Jeter-type with less power but more speed. Jemile Weeks, on the other hand, will probably hit for a lower batting average and even less power, but may steal a few more bases. He's a 2B to Beckham's SS, and various people will have opinions about which is more valuable, but in dynasty leagues where defense is not a factor, it's practically impossible to foresee which position will be rarer in 5 years, making it relatively unimportant.
5 years. That seems to me the issue. So here's the deal - Tim Beckham might very well be a better hitter and player than Jemile Weeks, but it'll probably take an extra 3 or 4 years for him to even make the majors. It's possible that the Rays will move him up faster, but it's unlikely that he will be a serious contributor until at least 21 or so. By that point, Weeks will be 25, and probably have started for 3 years, even if his production was less impressive than Beckham's will be. So to begin with, even assuming that Beckham will be more valuable than Weeks, you have to trade 3 or 4 years of no production for the hope of future production, with all the caveats of injuries and so forth. This is before one even considers that it is relatively rare for a rookie to produce significantly in his first year, meaning it might take until Beckham is 23 or 24 or 25 before he becomes substantially better than Weeks - in other words, in 5, 6 or even 7 years.
I'm not sure how far I'm willing to take this argument, but it seems like there is a case that if you believe that Weeks is within range of being as valuable as Beckham, even if you think that Beckham is ultimately the superior player, that you should pick Weeks over him because the current value outweighs the theoretical future value. A similar argument could be made for Jason Castro over Kyle Skipworth, or a few other people. How much do you buy this? At all?