BSB all the way for me, I think as much a product of timing and location - BSB just had a bigger career in the UK and *NSYNC didn't quite do it for me until too late.
I can see why slightly younger people might prefer *NSYNC though, when *NSYNC finally broke through in the UK (I'd say in 2000), BSB were on the way down.
But 1996-1999 BSB really were showing us how it's done. I remember rinsing one of those videos I got with TOTP or Smash Hits magazine that had "Get down" on it, and being sort of obsessed. That first album had some great singles, and that "Quit Playin Games" video? Little gay teen Diddy was really getting his life.
Then "Everybody (Backstreet's Back)" was a real pop triumph, and "As Long As You Love Me" too. And the sort of denouement to all that was Millennium, that felt like the real world-conquering moment with "I want it that way", I mean COME ON. I feel like that was the peak, and even though "Larger than Life" saw out the decade, I always felt like that was just like a sequel to "Everybody", and the peak was sort of cresting then.
Then a few months later, "Bye Bye Bye" was here and I was turnt. But I always found Timberlake's hyper-nasal vocals a bit annoying, none of them as cute as BSB in their early days, and for the Max Martin stuff, we had Britney by that point. I mean *NSYNC still had some great moments, "Pop" really was the one for me, and then they went down the tired old urban-courting image change attempt, Timberlake went on to bigger things, JC Chasez had a few decently intriguing singles, and that was sort of it.