My qualifications for commenting: Been training BJJ for about a year and a half, competed some, observed MT people train.
Neither MT nor BJJ explicitly involve any sort of meditation or suchlike. On the other hand to get good at BJJ you have to use you head. You have to think hard about what you're doing on and off the mat. You need to visualize moves and practice a lot. There is always more to learn with BJJ.
In competition I find that all other thoughts are totally gone from my mind and my focus is 99% on who I'm fighting and the rest on my teammate who is giving me advice. You pretty much have no choice but to focus on winning. Competition is really fun, you get to see what you can do when you go 100%.
As others have said there are other benefits to learning BJJ. I would imagine they get more pronounced as you learn more but as I'm not that good yet I don't know. Learning to value technique over strength, learning control, base, pressure, how to tone yourself down to roll with smaller/worse people, etc all probably carries some sort of mental benefit.
With MT, if you want to actually be good, you need to get a really good understanding of timing and angles and such. The pain probably focuses you in some way. I don't know much about MT except that it's harder conditioning wise than BJJ.
If I were you I'd go with BJJ. I'm not sure where you are getting this idea that judo is full of meditation and such. From what I understand it's generally trained much like BJJ except possibly harder intensity, more japanese names and obviously a lot more standup.