Online emulators are crapware. You don’t know what other code they’re running on your machine, you don’t know if you’re playing a legit copy or some random ass hack, and most importantly it’s a quick route to randomly losing your save data. Also those sites are far more likely to get targeted by copyright enforcement.
Plus, if you use a decent emulator, you can often tale your save files on the go. Retroarch can be a bear to set up, but I can play on my big monitor at home and pick right up on my phone later while I’m waiting at the doctor’s office or something.