Opera spent a lot of time and money getting their act together with the spiffy new Webkit version of Opera Mobile. But their users are a hard-to-please bunch, and apparently some weren't completely sold on the new design. So the older version of Opera Mobile is back in the Play Store, sporting the title "Opera Mobile Classic," for one last tour of the browser circuit. It's free, as always, and comes with the original's comparatively wide featureset. It appears to be compatible with devices running Gingerbread and up, and possibly more.
The newer version of Opera is faster and objectively better in just about every respect, but old users might be missing the original syncing via Opera Link, Speed Dial, text rendering, and a more (ahem) familiar user interface. Whatever your reason, be sure not to confuse it with Opera Mini, which is specifically designed for low-end devices that can't handle the more memory and processor-intensive Opera Mobile(s). Want to go the other way and be even more forward-looking? Then there's the beta version which grants access to bleeding-edge features before they hit main build.
If you find that one Opera or the other is better at rendering any particular page, there's nothing stopping you from installing more than one aside from a cluttered app drawer.