Well, there is no set rules for which sax will get more solos if there's 2 or more in a band.
I think that 2 reasons will dictate though… the style of the song and how good the player is. In other words one will simply just fit better for the song's style and the player's style.
Thanks for the input, Johnny. Having read the email you sent yesterday (Which Sax Should I Play?), I'm going to hit the nearest music shop and bust out a few tunes. I think, after that, I'll know. To be honest, it's seeing you rock the tenor that's inspired me to give it a try – thanks!
If you're leaning towards rock and roll, the tenor is more suited. Having said that, one of my all-time favorite sax players is Edgar Winter, who plays a very mean alto.