It's essentially the same tradeoff as having a hot wallet vs cold storage when it comes to bitcoin. Is the wallet provider going to run off with your keys and damage his reputation forever? Unlikely, but what if they get hacked or compromised by a government?

A device which is online all the time in the security of your home/office can't really be compared to some (probably) AWS hosted webserver just because both have an internet connection. One is entirely under your control, the other is not.

Do you like responsibility in exchange for control? If so, it's for you, if not, you're going to prefer convenience.