As far as epiphones, I just sold a studio that I couldn't get along with. It had a big baseball bat neck. The one I have now much thinner. Also the studio had a raw feel, the standard is poly. Can't speak for Gibsons as I've only played a handful.
I've got a Dot, and the neck is a bit thicker than my mate's mid 60's 335, but I've played them back to back, and after a few minutes with either I'm not conscious of the difference. The fretboards feel very similar (ie, flat).
Gibson USA uses Jescar FW55090 .055 tall x .090 wide
Gibson Historic uses Jescar FW45100 .045 tall x 0.1 wide
Don't know what Epihone uses but to my fingers it definitely feels not as tall as even the Historic Gibson, I'd say it is closer to Dunlop 6150 .042 tall x 0.102 wide
Interesting feedback - virtually all of the Epiphones (335 or other) that I've played over the last 10 years have had slim-D profile necks?! They're reasonably wide at the nut (1-11/16" I guess), but definitely not chunky.
The only exceptions I can recall are a '58 flying vee I owned, and a firebird studio I played once?