Can a beginning player learn as fast on a tenor sax as one can on an alto saxophone?

I always hear that people should begin on alto. Other people say that if you're grown (I'm 34) , then tenor should be no problem. I've played trumpet for the past year, so I feel like I have good strength. I like both alto and tenor. I feel like maybe I won't be able to play very fast on the tenor due to it's being a bit larger, but I could be wrong. Will teachers teach a beginning tenor student? Any thoughts?