BPM question

I recently got into a slight argument with my vocalist on tempos and BPMs. And, I think maybe we were both right, to varying degrees. In straight 4/4 time, don't we count BPMs as quarter notes? What about cut time? Or 2/4? For example, the song in question is Mrs. Robinson (The Lemonheads version). Give a quick listen, if you will, and let me know what BPM number you would assign. To narrow this down, we were arguing over 108 vs. 216. As you can see, the second number is twice as high. Obviously, a difference in which notes to count.

Would you rate this tune at 108 BPMs or 216?

BPM question