Fireworksboy is right that the Sheraton's pool is more kid-appropriate that the Westin's. The Sheraton pool has a winding corkscrew enclosed waterslide and a huge pool with games and volleyball, etc, etc, etc. The Westin pools are nearly empty and surrounded by scads of adults quietly reading or having drinks.
It is very important to know that these two hotels are all part of the same complex and are easily walked to in a matter of 2 or 3 minutes. For all intents, you could imagine that it is all the SAME hotel. So, if you really far prefer the Westin Bed to the Sheraton Sweet Sleeper, for example, stay at the Westin and then walk your 4 year old over to the Sheraton pool the next day. Everybody does it.
My last point of distinction b/t the two hotels is that the Westin Club Lounge on the top floor of Breakers Cay was really a major added plus for our stay. The attendants were exceptional as was the quality of the food and drink. We were very impressed. I do not know if the Sheraton has an equivalent. If you're a Plat, that might make a difference.....