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It just depends on what types of devices your users are going to be using and how large the map area is going to be. For modern day web maps viewed on desktops/laptops, I like to use 1024x1024. If your map is going to be viewed on a desktop computer you are probably looking at a resolution of 1920x1080. So if your tiles are only 256x256 or 512x512 it is going to require something like 10-20 tiles to view the entire map. All of those tiles means more connections which slows things down a bit.
I have been using tiles of 1024x1024 and it seems to be working out pretty well. The number of connections is much lower because not as many tiles have to be downloaded. The overall download size is about the same, but fewer connections means it feels faster.
If your map is going to be used on mobile devices then 256x256 would be the way to go.
I checked Google maps this morning on my desktop and they are using 256x256. But I'm guessing that a majority of their usage is from mobile devices.