Opera Mobile is the one I use most often on my Eee Pad. I like it mainly for it's lag-free keyboard entry. With the stock Browser, there is some lag when typing on various web sites, especially the Android Forums web site. Also, the cursor is not in the right place on the stock Browser. I have none of these issues on Opera Mobile.
Opera Mobile does not provide full functionality for certain web sites. Any web sites that use Disqus for comments does not allow me to enter comments if I use Opera Mobile. I have to use the stock Browser in order to add comments via Disqus. I sometimes use the stock Browser for sites like this and other sites that Opera Mobile has issues with.
I do find that the latest version of Opera Mobile is excellent. I had issues where text I have entered such as posts on this forum just disappear on me. This latest release of Opera Mobile seems to have fixed that issue. That was the main reason I used to use the stock Browser a lot more. Now that this issue is fixed, I use Opera Mobile a lot more now.
Another great feature is that my book marks are synced between my tablet and phone. I primarily use Opera Mini on my phone as the Mini version works better on my phone than the Mobile version.