Hi,
Yes I have the Champion 600, never tried the Epiphone. At the price point I think the Champion 600 is a great buy. But it's not without it's problems - the most significant ones being a hum even on zero and a pretty awful speaker.
To my taste the amp sounds great with single coils but not so great with humbuckers.
There's quite a bit of stuff on Youtube from a guy who trades under the name Alnicomagnet on the UK ebay site. He has designed some mods for the Champion 600 and the Epiphone as well. In fact his ebay listings are quite informative.
From what I see the std amp actually has a Blackface type tonestack it's just that you can't adjust the Treble and Bass. It can be modded to the Tweed style circuit and apparently that makes it sound a lot better with humbuckers.
The Hum is down to the placement of the Power Transformer and Output Transformer - they are too close. Turning the OT through 45 degrees helps this.
I see that Mercury Magnetics have gone to town on this amp but at $275 for the upgrade kit it's kind of more than the amp costs.
All the above is based on reading - I actually plan to do the Alnicomagnet mods over the holiday period.
Pete