For MusicBrainz you can try to change the File -> Options> - Tag Sources settings to
"Original"
But there is no guarantee that you really get a bigger cover. It always depends on what quality and size is available at the source (Cover Art Archive). Please see the details in the documentation.
Several comments in the Discogs forum include something like this:
The reason for the 600px max is so that the image are a representative image for recognition but are not high-res enough to be considered reproduction, which could incur law suits. It's annoying not to be able to see high-res images, but there is a reason for that. Discogs is looking for ways to be able to display higher-res images, but unless copyright owners and lawyers start taking a different attitude to online open-source databases when it comes to copyrighted material, that's unlikely to change any time soon...
I could not find any official statement from/at Discogs.