Hi there, thanks for reading and for the reply!
I have very little hands-on experience with the MMX 300. I've never reviewed them or commented at length on them, though a couple friends of mine enjoy them. I do have extensive experience with several of the Beyerdynamic headphone models it is based on. I don't really feel comfortable commenting on the MMX 300 directly, beyond saying that I vastly prefer that the H6 Pro has a detachable mic. I did spend a bunch of time reviewing the MMX 100, and while it has a nice mic, its ear pads are too shallow for a comfy fit.
Unfortunately for reviewers and customers, there isn't much correlation between price and quality in the gaming headset space, or for audio products in general. The Cloud Alpha has a worse-sounding microphone than the H6 Pro, but on sound quality it's not at all that far away.
Most closed gaming headsets, the H6 Pro included, will have a boomier, bassier sound signature than the 599's you're used to, and might take a little brain adjustment. The H6 Pro is in the same category of quality, but its excellent detachable mic is a big part of its price/value. If you want to stay in the Sennheiser family but spend less money, you could always check out the H3 instead if you're mostly going to listen and not record/chat, and you don't mind the permanently attached mic!
Or if you're mostly playing single player stuff, you could always look into nice closed headphones like the AKG K371 or something. JBL's Quantum range of headsets is also based off of the same Harman Target sound research and I find them enjoyable.
Hope something in there helps you out. Sometimes headsets are a journey you have to take to know your own preferences. The H6 Pro seems like a safe bet based on what you've told me as long as you don't mind the additional bass...but you won't know absolutely for sure till you try them on your own ears.
Cheers!