Wow, hmmmmm. Good question and it draws on my "aural memory" of the Lonestar. Let me start with my bias. To my ears, the two best clean tones I've heard from modern multichannel non-boutique amps, short of classic vintage Fender cleans, probably are the Lonestar and the Bogner Shiva. My opinion only, not looking to start a flame war. Again, I am not saying those are the best clean tones available, but for my need of multi-channel, mid market, manufactured products, I loved both those cleans.
I'd say the GF45 clean is more like the Shiva's than the Express' is like the Lonestar. How's that for a vague, non answer? Overall, I'd say the GF45 has better tones than the Express. It is richer, more complex, more "professional". I'd have to say the 6v6 GF45 is kind of like a mini-Shiva. I really dig it. I actually traded a Royal Atlantic for it and haven't regretted that trade, although I loved the RA. (side note-I think the RA's clean tones were more Lonestar ish than Express and damned good, as good as the GF. It is a beast of a head, but worth considering if you want a Lonestar type clean.)
I think the GF's cleans are a little rounder, richer, chewier than the Express. So, if I were voting on great cleans, I'd give the nod to the GF over the Express. I think the GF's gain tones are more Marshall thick, while the Mesa Express' are a little more modern, cutting, edgier. So, if you play more metal or tighter more aggressive gain, I'd go with the Express. Of course, the Express has two modes per channel, plus the EQ options, so it has more flexibility and available variations and options. So, if you like a wider palette of tones from one amp, the Express is more versatile. On the pure core tones, I'd nod to the GF. When you weigh in flexibility and options and versatility, the Express has more of all that. What you do with that info, I have no idea?
I wanted the more Marshall vibe in the GF as a complement to my Mark V. The Express is my small, grab and go amp or tiny gig amp. So, I had reasons for each.
Frankly, if you are considering something in the GF price range, and want great cleans, more high gain and versatility, I'd take the Mark V over the Express every day of the week. I call the Express "the mini Mark V"- it is less of everything the mark V is, but with a lot of the versatility.... (yes, I realize the power tube sections are completely different, but to me, the E525 is like a scaled down MV light amp. I suspect the E550 is even closer with the 6L6 tubes instead of EL84s). If the price and weight are in your range, that's THE amp in my opinion. If you are at a lower budget and like the light, grab n go- the Express is a really great little amp.
Sheesh, I have no idea if I helped at all, or even answered your question. Again, I am not issuing any kind of royal decree or looking to start a flame war over these amps. Just offering my opinion.
Good luck,
Brent