As in most cities, Boston has more than one "centre". The Sheraton is in the Back Bay, very convenient to Copley Plaza, Newbury Street, Charles River Esplanade, Fenway Park, major Museums, Symphony Hall, Christian Science Plaza, etc.
Although you could walk from Sheraton to Faneuil Hall area (2 Miles/45Min walk), you would probably want to take the "T", uber or cab.
Two different areas, both are "Boston".
I have stayed at ES/Logan several times, with 2 kids, because of convenience to airport for early departure. Serves that purpose nicely; however when you walk out the door, you are still, in a neighborhood surrounding the airport. When you walk out the door at Sheraton, you are very much, in Boston.
Finally, if you have 3 kids and you are going in the summer consider that the Sheraton has a very nice pool with retractable roof!
Just the thing for cranky kids (or parents) after traipsing around the city all day! While the Logan ES does have a pool, it is your typical small, indoor variety.
I would choose Sheraton if you are getting rates similar or even close.