I have stayed in both of these properties and each has their benefits. First it depends on which airport you are coming in from. NRT will take you an hour to get into Tokyo via Narita Express train. You would take it to Shinagawa station and then that is where your next path is dependent upon hotel choice.
Sheraton would be a ~1200 yen cab ride from there or you can take the yamanote line 3 stops away to meguro and take the metro one stop and walk, about a 5min walk (don't know if that is what you'd want to do with luggage and children though, so take the cab).
For the Westin you would take the yamanote line to Ebisu and then you can walk about 8min to the hotel (moving sidewalks about 70% of the way) or catch a cab. The exit from the station puts you on one side of a business park, hotel is on the other side.
The Westin is nicer but more expensive. It has a really nice club lounge and a big/pricey buffet restaurant among other things.
The Sheraton has no lounge but gives you free breakfast in their restaurants, which is a full buffet as opposed to the smaller club lounge option at the Westin.
Also as mentioned, the Sheraton has a shuttle in the morning that you can take to Shinagawa to get on the Shinkansen, which is nice. I'd probably choose the Sheraton between the two.
If you're coming into HND, I would choose Sheraton Yokohama. Next to station and can take the airport bus instead of trains so you won't have to lug your luggage.