There is a school of thought that food processors can alter the taste of some things. They make onions taste weird in my experience. I remember when I was a kid working in my uncle's butcher shop that I found the mincer gave a particular taste to meat and still notice this on all commercial mince meat. Citations may be required but I always put this down to energy and heat generated by the speed these machines work at. Maybe if you put the food processor on a slow speed. Some vegetables, carrots being a classic example, taste different depending on how you cut them.

Ideally, a decent 8-10 inch very sharp chef's knife with a broad profile — i.e the distance from the sharp edge to the top is at least 3cm — is best for dicing finely and a bit of practice will have you chopping very quickly. The only tips I can give are these with chillis. Slice them in half length ways, de seed them, then finely and carefully slice them lengthways. Then, the reason for the broad profile on the blade will become apparent — basically hold the sliced chillis flat on a chopping board with three fingers with your finger tips slightly bent under use the knuckles against the flat edge of the blade as a guide, chop and move your fingers slowly along the length of the chilli or push it forward with your thumb. Bit of practice and you'll look like a veteran dicer.