I would think that leaving this wallet open 24/7 would be less secure because now you have a program (written by mostly junior/incompetent devs) leaving a port open to the public internet. Doesn't it have to do this to keep the network running? I have a feeling at some point a vulnerability will be found and this wallet will get hacked and my machine will be compromised. But I still leave mine open anyway. Or maybe we'll get lucky and our devs won't touch the networking code. Best to leave that to the experts.