Never stayed at the Sheraton in Parsippany before, but I have stayed at the Westin Governor Morris before.
The Westin is an old hotel. As a platinum, I was upgraded to a very large suite with a Heavenly Bed. The bathroom was not a Heavenly Bath with the two shower heads. The rooms have high-speed internet access.
The furniture and decorations in the rooms are a bit dated - but the hotel has a "classic hotel" feel to it - a nice change.
The entire hotel is non-smoking.