Water Mill, Amagansett, or Bridgehampton for summer home?

Better for what?

amagansett is a tough drive

Water Mill and Bridgehampton are very similar. WM may be a bit more relaxed, and is a marginally easier drive from Manhattan. Also, depending on your price, WM probably has more properties with waterfront views or that are actually on the water than any other town in the Hamptons (due to the fact that WM wraps around 75% of Mecox Bay). If you want wooded privacy or farm views, both WM and Bridge offer plenty of options.

Bridgehampton is home to the polo tournaments, classic car shows, etc. And Bridge has a real Main Street with several really good restaurants and shops. WM's retail is MUCH smaller.

Amangansett is very nice, and maybe even more relaxed than Water Mill. But it' almost at "the end". So add 30 to 90 minutes to your commute (ie., 30 to 90 minutes past Bridgehampton).

If you're questions is better re prestige, it's a toss up.

Bridge has historically been #3 to Southampton and East Hampton
Water Mill is, however, the most expensive town based on median home price.
Amangansett has a lot of quiet money that craves the beach-y scence.

If you want a scene, head to East or South. Otherwise, it's more about feel and comfort than being "better"