I have stayed in both, and much prefer Le Meridien. It is newer, more luxurious, and with much nicer, more helpful personnel (my experience.) My room at LM was a spacious palace, with a huge marble bathroom. My room at the Sheraton was somewhat dated, and more Holiday Inn-esque.
LM is literally right across the street from the Central Station, whereas the Sheraton is a 5 to 8 minute walk, through some winding streets. (The first time I was headed to the Sheraton, I got in a cab at the train station, but the cabbie refused to take me there. He simply said it was too close for a cab ride, and gave me walking directions. Kudos for his honesty, or perhaps just for his reluctance to give up his place in the cab line for such a short fare.)