I've nearly finished my basement home theater but I'm having a bit of trouble with subwoofer placement.

The floor of the basement is concrete so I have a feeling that is the main problem...

I've tried placing the subwoofer directly behind the seats and in the corner of the room behind the seats (about 8 feet from the listeners?). The corner of the room seems to work best but both locations produce completely different vibrations.

Which is better?

It is almost impossible to answer your question with the information you are giving us.

How about room dimensions?
How do youi define "different vibrations?

Does one location sound like a "one note" sub?

The crawl around test might be a good idea here. If you can, put the sub in your listening position. Then crawl around on the floor to find the best sub response. It will get you close.
Also, just moving the sub a few inches out from a corner or wall can make a pretty significant difference.