The LMP is only about a 6-7 minute walk to Leicester Square (especially if you shortcut through the Piccadilly Circus tube station to avoid the crowds and crosswalks in Piccadilly Circus itself), so you're not giving up much there. And IMO, it's a little more friendly to the needs of a business traveler. The Sheraton PL, OTOH, is another 15 minutes of walking down Piccadilly past the LMP. So while it's now the nicest of the three, it's a pretty long walk to LS.