Isn't your mini 34" tall or so? If so, he most likely needs a 3 1/2" bit, not a 4". I have a 34 inch and 36 inch mini that I drive and they both wear 3 1/2" bits. I agree that your guy looks like he has a bit too big of a bit still. A 4" is what I use on our 42" tall shetland pony.
I use a single jointed half-cheek snaffle, a french link half cheek snaffle, and a mullen mouth full cheek. I love all of them, but it just depends on the horse for which they prefer. The gelding mini that I use has a rather small palate so he prefers the french link, while my mare goes contentedly in a half cheek.