I have been to both also. As mentioned if you like the "old feel" then choose the Sheraton - I do not and would choose the LM in a heartbeat. Very nice corner room with great views and loved their Club Lounge - felt like your own little restaurant with great views. In saying that the Sheraton was easier to just walk out the front doors and be in the action. Stay at both

.....and of course price might matter too.