I'm pretty familiar with both. They're both absolutely fantastic.
My take
The Monique is gorgeous sounding. This can be a good or bad thing. "Romantic Tube" is how I'd describe it. I think it works well with cabs that aren't too big and loose in the low end. For instance---the Monique sounds really nice with my Flex cabs.Kindof widens the envelope of the notes. They are very tight and punchy. Opposite of a loose low end. Some guys dig it---some don't. Which is how it should be. With my 46, which is warmer in the mid through the upper bass---it's not a good match. WAY too much of a good thing. The Monique top end isn't very forward sounding---again, it's on the romantic side. So--a cab that is a bit bright in the treble is a nice offset. The function of the eq is more subtle to me. The eq won't change the essential character. The sensitivity control is really cool. That DOES change the sound. You can lean toward solid-state tightness and uber tubey romance. But it still is a warm, romantic sound.
I'm just mentioning my cabs because that's what I've heard them through! None of them are perfect but they do have different characters---so it's easier for me to make comparisons.
JGR's is a different animal. More focused in the lows and more extended in the highs. The Studio 1200 liked all of my cabs. It seemed to bring out the character of each. Tubey, but in a studio focused tubey way. It's pretty cool---it can get closer to a studio hifi sound, but you can push it into the grunge range, too. The eq is much more to my liking---12 o'clock is 12 o'clock. Five bands, I think. Well chosen eq points and less interaction between bands than I would have expected. The 1200 is maybe more to my taste---I'm a pizz funk/fusion guy. No boom for me, please. Focused tight low end. Fast,fast,fast. But more of a hifi take on a 60's or 70's funk/r&B sound.
I'm more familiar with the power amp section of the 1200 as I'm using it in my amp. It slams like the best class a/b. I'm not as familiar with the Hypex module that Jule is using. My experience with the Hypex modules is that they're exceptional.
While JGR's might be my preference, I can't remember when I've had more fun than using the Monique into the 1200 watt Ice and into a Flex 210.
Both are stellar.