No single character is better in every situation, as FireSword pointed out. However, in general, I think Spaz has a few advantages. Spaz's double jump when he's running at full speed is higher than Jazz's uppercut, and double jump often makes it easier to quickly navigate a level, and being able to quickly get to a carrot/power-up/flag can make the difference between winning and losing a game. Jazz's helicopter ears can be great for really long jumps, but they work by slowing down your fall speed, and in JJ2, speed is by far your greatest asset when it comes to dodging enemy fire. Lori can do some neat tricks, but her inability to jump as high as Jazz or Spaz, and the fact that many levels are not designed with her in mind makes her too specific for most people.

So even if Spaz isn't truly "better" than Jazz or Lori, there are some good reasons that he's most popular.