Mozilla recently showed off a new browser they're working on for the iPad called Junior. Since the browsing engine is already locked-in by Apple, most of Mozilla's work is on the design front, namely by eliminating tabs and an address bar from the primary browsing experience, and instead tucking them behind a separate menu.
When browsing, there are two half-circles midway through the screen: one for navigating backwards, and a plus symbol that will help you get to your next destination. That plus button can send you to a tabs/search/bookmarks screen, which means those tasks don't have to hang around in your main browsing window all the time. There will also be some kind of multi-user support, so browsing preferences and history can change accordingly. Mozilla also promised that Junior will be optimized for the big Retina display.
In its current iteration, Junior is defaulting to Bing search, but an earlier demo of their next desktop browser showcased a great new way they're working to promote search engine choice. Not only was Mozilla ditching the dedicated search box, but after launching into a search, a few small tabs would pop up on one side which would let you send to other engines for the same query. It's easy to imagine that sort of thing findings its way into Junior, but for now they're separate products. Mozilla has already released mobile versions of Firefox on other platforms that have tab syncing over the cloud and add-on support; hopefully those features will find their way into the final release of Junior, but it's hard to say at these early stages.
The Mozilla guys went so far as to say that the current Safari experience on iOS was miserable, despite still being the best default mobile browser. I'm not wholly convinced that Junior will be able to offer something that's infinitely better. DO you feel like tabs and the address bar cramp the viewable area when browsing on the iPad? If there was anything you could change about Safari on iOS, what would it be?