Owned both. Stock, and modded. I agree with Opus88 that the 600 sounded somewhat lifeless. During all the years that I owned the 600, I could never understand the AHC review in TAS in which he describes the 600 as very dynamic. I would have to disagree. It will play very loudly as it has tons of power, but the music does not MOVE. It sounded somewhat "lifeless". So why did I keep it for years? Beacause it was a very full, and robust sounding amp with nice tonal colors. This was exactly what my Maggie MG3a's needed to not sound too thin, and it was all I could afford at the time that had that kind of power.
"Does a modded 600 change the nature of the sound from the stock model?": No, but it will be a little more refined sounding, and maybe a tiny bit more agile sounding.
Interesting that you found the 600 more lively sounding. In my experience the 300 sounded a little more agile than the 600 (maybe your speakers really need the extra power). But I don't think that it was the result of actually being a faster amp. The 300 was not as full or dark sounding as the 600, and the psychoacoustic effect was of being "faster". An Olympic sprinter running the 100 yard dash, would probably look to be going faster than an NFL linebacker running at the exact same speed.
BTW, the 600 gave me one of the most important and memorable audio lessons: I bought a pair of incredibly difficult to drive Stax F-81 electrostats. I thought that the very powerful 600 would be just the ticket. The sound was mediocre at best. One day, a friend brought over a lowly Dynaco ST-70 pure tube amp (35W/ch) in stock form. The Dynaco blew the pants off the Moscode 600. I could not believe it. All of a sudden, there was refinement, and although it would not play very loud at all, the music MOVED. It was an incredible experience.
The Moscode was treplaced by a Berning 1001 (?) pure tube design, and I never looked back. (Manley's currently).