Yes, I have the same problem. The difference is that I'm right-handed, but my left arm is fisically more developed and has practically half bigger bicep. And nothing can change it)) Not even the hard training.
I'm thinking now that it is a fisical speciality of a body. And I have the same with the whole body. The left part has more muscle mass than the right.
Well thats what I was getting at that stabilization is a good thing for overall but too much stabilization and your actually taking focus away from targeting a specific muscle as much. Benching with Dumbbells isn't bad but I personally find that Benching with a barbell is better. I dunno I've just always got a better feel from a barbell and there is a good motivational factor too it because you can bench more weight with a barbell than with dumbbells because they are separate and require more stabilization. And with that when you see that your benching that much weight you feel a bit more proud of yourself that you can achieve that and will wanna keep going and push the bar (no pun intended
). So yes the bells are definitely better than a machine but Barbell is the better of the two for targeting your chest muscles themselves. But again it depends on what type of results you want and as a girl you probably don't want massive pecs do dumbbells are a good option for you in that you'll get a good triceps and shoulders work out with the dumbbells as well because of the higher stabilization factor 
.
. Its like a P90X program. Its something they have been advertising on tv for a few years now as an EXTREME work out program that you need to buy like a 10 dvd set for. You follow what they tell you do to and then you get ripped, simple enough. Except for the actual workouts because from what I can tell they are extremely brutal. They most likely will give you results but you need to stick with them through the whole 9 yards in order to get the results they promise. You will need a strong will to get through it but if you do then your good.