Westin lobbys smell better (the more soothing white jasmine scent). They also typically have better beds/sheets. They also appear to emphasize more on the shower/bath experience (read: better towels), the gym and healthy food options .. all in relation to their 'be well/healthy' motive.

Sheraton Grands are more likely to have exec lounges & a busier lobby scene ("connect"), and not just because of Link@Sheraton. They tend to have better restaurants, though not always. They usually have better/more casual bars too. The rooms are more contemporary with a more "slick" feel but wouldn't say are as "soothing" as the Westin ones particularly around the color tones and the bedding etc.

just my 2 cents