The capacitor with the 250V AC rating is an X and Y rated capacitor and is capable of being applied across the incoming AC in your house. It's bigger because its reliability is much better i.e. it won't form a short circuit if it fails.

The capacitor with the 250V AC rating is an X and Y rated capacitor and is capable of being applied across the incoming AC in your house. It's bigger because its reliability is much better i.e. it won't form a short circuit if it fails. Here's the idea behind them: -

As you can see a Y rated capacitor is designed to be between line and earth thus a properly designed capacitor will not short line to earth (electrocution possibility). The X rated capacitor can be put across live and neutral and does not need a fuse i.e. it does not pose a fire hazard because it fails safe = open circuit.

The capacitor on the left is therefore bigger because it is more reliable in these scenarios.