Is there any great difference between choosing one over the other? I understand that barbells hold significantly greater weight than a dumbbell, but regarding stabilizer muscles, etc., wouldn't dumbbels be a better choice? ISTM that one would also not be able to "cheat" dumbbells by using their dominant arm to lift a greater share of the weight than their weaker arm.
Finally, I'm planning on training at home (at least until I can get my numbers up to something respectable before heading into the gym). I'm planning to get some dbells and weights to start my program (planning on beginning with overhead squats, deadlifts, bent over rows and lunges and shrugs. If I ever get a bench, I will work in the benchpress as well) to get some additional strength for MMA - would dbells be more useful in this instance?