Hi Alan, I've been both ways several times and you are correct, the east entrance is a faster route. The south more scenic, but slower due to traffic and such. I usually drive straight thru (no TM) and stay in the park so we take the east entrance route. either way it's a blast obviously. Our favorite time is late May when the animals are all in the Lamar Valley, love watching the wolfs. Check out this site if you haven't already. Lot of info in the forums.
http://forums.yellowstone.net/