I have competed in boxing , Muay Thai or Thai boxing, and mma. I coached a high level athlete in mma as well, 2x UFC and fought 9 time overseas etc.
Boxing is one dimensional and is very brutal to the head because of the length of the fight and basically hitting till someone goes down or the fight ends. MMA is the triathlon of fight game. You have to box, kickbox, wrestle and do Ju Jitsu. Within MMA , the boxing game is made more brutal by the smaller gloves. Less blows to the head but hard trauma. Its actually safer than boxing but overall to the entire body and skillset, mma is the most complete.
However, in my fight experience including training in Thailand, Muay Thai is the most brutal and 'toughest' sport. It includes boxing, kicks, knees, elbows. The amount of hardening the shins and forearms go thru literally transforms your bone structure. I used to kick a 300 pound sand bag with my shins 3 times a week for 10 minutes at a time to get my shins able to fight and use them without alot of pain. Add Elbows and knees and 5 3 minute rounds and I believe the Top Gun of the fight world for toughness and technique is Muay Thai. If you get hit or hurt, you cant shoot a single leg and start to grapple, you have to stand and BANG.
The cardio involved is different and more anaerobic than cycling.