Underneath they are similar, however I was in the same boat as you. Lutris first however after installing a few apps I moved towards heroic.

Heroic is easier to manage your library requires less tinkering and as a benefit for steam deck owners, has controller support by default and native integration with epic games store.

Lutris works better for non platform games, like old PC games from CDs or EA App.

How I’ve been moving my games over is rebuying games I would be gutted to loose like Fallout 3, and Doom 2016. Then waiting on sales for the rest. Also Amazon Prime has free gog games so you maybe able to get a handful of games every month to move over