I downloaded ÜberTwitter to my BlackBerry recently - it does so many things that TwitterBerry can't.
 
These are the ones I like in particular:
 

1. On the ÜberTwitter icon, the umlaut accent marks change from green dots to red stars when new tweets come in, without you having to launch the app
2. Tweets are appended with your (approx) location on a Google Map - don't worry, it's optional but can be useful for campaigning, events, or just showing off when you're on holiday ;-) When readers click through, they see something like the above screenshot
3. Photos are embedded in tweets without having to click through to them - although you can, if you want to enlarge or go to the hosting site
4. You can take photos and post them directly within tweets. No need to set up a separate account anywhere, ÜberTwitter takes care of it all by posting an ÜberPic complete with the number of views
5. You can look at a user's timeline in isolation
6. There's a retweet command (TwitterBerry had me doing a lot of copying and pasting)
7. Reply all - useful for when you want to reply to a tweet containing several usernames without keying them all in
8. Reply to DMs as DM, not @ (to avoid those awkward moments - what Auntie used to call "showing your petticoat." We've all done it...)
9. Hashtag search
10. Trending topic search
11. Search friends and followers (and your friends' and followers' friends and followers... Huge time-sink alert!)
12. Look for twitterers near you: "Everyone near you"
13. It updates differently. Whereas TwitterBerry automatically updates to view the most recently posted tweets, so that you have to scroll down and read the rest in reverse-chron, ÜberTwitter saves your place at the last tweet you viewed, then you can scroll up and read in order.
14. Shows the bio of a user when you click on one of their tweets.
15. Favourites: you can mark them and view them, plus those of your friends (encore huge time-sink!)
16. You can delete your tweets
17. There is an Unfollow command
18. You can follow conversation threads
19. You can select "load more" to view even more tweets from a selected timeline
20. It shows which twitter client other twitterers used to post their tweets (I take a nerdy interest in such things and know others who admit to the same...)

 
Automatic URL shortening is promised for the next release - excellent!
 
It would also be nice to have:
 

1. Umlaut accent marks turning a different colour when "@" replies or DMs are received, or getting an asterisk like the BlackBerry Facebook icon does
2. Ability to view sent DMs as well as received ones
3. Ability to post short sound files in tweets

 
Although I really liked TwitterBerry, I've taken to ÜberTwitter straight away - it's helped me find so much more information, and easily too.
 
Have you tried it yet?  Which features do you like/use a lot?
 
Download ÜberTwitter here.