xsplit can do that easily, just click on both local record and broadcast on twitch in any order. I don't know about OBS. but remember this will require to encode 2 videos at the same time so it will obviously require more CPU usage

another solution could be to use dxtory and record in either, a lossless codec like Lagarith / MagicYUV / x264vfw or a lossy codec like x264 this will only record the game and not your splits/layout or what you say on mic

For separate qualities you'd have to have two instances of OBS running, where one would do the local recording and one would handle the streaming.

A lot of people use amarectv to do this. Maybe someone has a guide out there to set it up, because it's not exactly easy. Amarectv can record lossless .avi with the lagarith codec which you can process after the fact.