You're right that it's not really fair to compare the two. The Achilles' Heel of the contra-alto, in a nutshell, is range, which is why the Bb/C overtook it ca 1910.
However, the process of overtaking is not as simple as all that. It was mostly due to the composers, who were writing parts that were ever higher in register.
It would be disingenuous of me to claim that the contra-alto is all smooth-sailing in terms of playability. It's a temperamental instrument in the high range. F above high C is high C on the Bb trumpet, so consider where you are in terms of stability. And each horn has its little idiosyncrasies, so from the 2nd octave up, you'll be using various alternate fingerings, just as you do when playing "French" horn. And despite how free-blowing the instrument is, it's a small-bore horn. BUT- the rewards vastly outweigh the cons. The sound is raw, visceral, exciting, has character. And in terms of playing, it's like flying a biplane, with no instruments, and with an open cockpit. You're always on the verge of losing control. And that's how I like it.
The late Artie Shaw once said, "If you aren't making mistakes (he meant playing beyond your ability), then you aren't really trying."