For better or for worse, you might want to take into consideration that Savannah's St Patrick's Day parade is scheduled for Friday, Mar 14 this year.
http://www.savcvb.com/events/?ms=631
That's affecting hotel prices in SAV for the later part of your trip (I'm surprised that the Westin's not already sold out), and it will definitely be a busy few days around town for that very popular event.
I'm not a golfer, so my opinion doesn't count for much. But I'd think that Hilton Head would be the better pick for that aspect.
It's a very long drive from either of these hotels to CHS. Likely more than a couple hours. Only about 45 minutes from the Westin Hilton Head into downtown SAV, though. And there are plenty of great restaurants in SAV, too! (Not that Hilton Head can't provide a good meal on its own.)