I could go into deep specifics but I won't because you can goto the team developing each program to compare specs.
From experience. Apollo can do a lot more accounts such as MSN and ICQ and .Mac. Thats about it for pros for me. This program crashes a lot and I mean a lot, sometimes just trying to connect makes it crash. I've noticed too that the more accounts you try to log on to the more unstable it gets. I think after 2 accounts it becomes fairly unstable. It often too locks up your phone completely when trying to chat with someone. I've had nightmares with apollo, but i cannot complain because its a free program and the development team has put a lot of work into its development.
Mobile chat, even though it only does AIM. Is far more stable and has an actual option menu for turning on and off (vibrate, auto reconnect(this makes this program far superior to apollo), sound and pop ups). Apollo does vibrate but i haven't been able to figure out how to turn it off, I don't think theres a menu for it, correct me if im wrong and it doesn't turn off by simply putting the phone on no vibrate silent. I've had mobile chat online for days on end, sure it disconnects a lot and crashes sometimes but the reconnect feature makes it far more stable than apollo.
Overall, Stick to mobile chat, its the best we have so far. Still many things needed to be added, and issues needing to be resolved but it will give you a nice experience for now.
But with all honesty, Since I do heavy MSN , Yahoo and AIM all at the same time, none of the these programs would fit due to non yahoo support. Its coming but its not there yet. (iPhone.beejive.com) works great. It has loads of options and a 2 hour timeout and you still get your messages if your connection to edge fades for a couple mins. A tower near me went out for about 2 hours and when it was back up, I had about 29 messages from all 3 accounts just waiting there once it did "checking connection".
I think I'd have to agree with the MobileChat as a good app. I liked the stability of it and it seems to stay connected. Chat programs for the iPhone are still in their infancy so we got to give them time. All I can say is to try them both out, seeing as how you will not be out any money and see which one you like the best!
Its really odd cause it just started a week ago for me. I am gonna try apollo and see what it does, as far as connection and freezing . Beehive is great it works well and is easy to use but I like the idea of a native app, running in the background with notifications . I might just give up and carry a sidekick as well cause using aim an MSN are important to me. I don't see why Apple couldnt have given us an iChat Mobile.....