A lot of your MMA ground fighting and throws are judo and/or jiu jitsu based. MMA would give you a bit more rounded training, including strikes and kicks, while judo would focus more on the throws, chokes, holds, etc. A big selling point of judo is that, since it is very wrestling-oriented, you can practice full-strength and full-speed without taking each other out of class with injuries. There is no substitute for full-force practice. Anyone can throw a partner, who nearly jumps over your hip for you, but throwing someone who doesn't want to be thrown is much more difficult. You will fight like you train.
My advice: Sit in on a couple of each classes as an observer. Try to determine how judo-oriented this particular MMA class is. If the instructors are judo players, you may find the MMA kills two birds with one stone. If not, consider whether you can take both. The judo background would definitely add to your stability and balance.