I understand that, in order to cook chicken safely, the chicken has to be 175f or 79c.
But is there a temperature for the different cuts of chicken that improves the flavour of the chicken?
The USDA recommendation for a safe internal temperature is 165 degrees for chicken. The breast, being leaner, shouldn't be cooked to any higher than that or it will dry out and be tough.
The thigh can be cooked to a slightly higher temperature (165-175). That is the Kitchen Network's preference for taste and texture (link here). Getting the thigh to a slightly higher temperature (and keeping it there for longer) helps the collagen break down, which will make it more tender and taste more moist.
You will never find any chef with culinary knowledge to cook chicken as high as any USDA recommendation. I have never heard of 175F recommended by anyone! Even 165 will get you a sideways look.
150F is a minimum and I shoot for 155. It's safe and real cooks won't laugh at you.