I too stayed just last month for both.
I'd say, Westin is modern, Sheraton is classic style both in nice way.
Agree with moondog' comment. It's quite accurate. Once you are
on the floor, I didn't feel that I am in the old building. Just don't open
your eyes until you go into the lift.
For a tourism, I really think St. Regis is much better if you can justify, but
if not, Sheraton maybe a good choice.