Well, both are small aviary species and I am very glad you have decided to get a pair because neither do well on their own (meaning as only birds). They both get along with the opposite or the same gender but I personally recommend getting a male and a female because, as they are monogamous and mate for life, these birds do much better from a psychological point of view when they have a mate than when they have just a friend. Neither species bonds deeply to humans but they are VERY friendly and can learn to trust and love their human as another flock member.
Budgies are more noisy because they chatter all day long and, although I enjoy this constant background 'chit chat', some people get fed up with it after a while. Cockatiels are not noisy at all, especially if you have a pair because you will mostly hear the male calling when hormonal and the female not at all (females only call -and can do it incessantly!- when they are alone and hormonal). Both need the same kind of diet (whole grains, veggies and greens for breakfast and grass seeds for dinner with some good quality multivitamin/mineral supplement given regularly -twice a week does the trick), cage (a large flight one) and light schedule (strictly solar as they are VERY opportunistic breeders).
The biggest difference comes in the colors and, to a lesser extent, their price. Budgies are quite inexpensive (you can find them for free or a very nominal adoption fee in CL all the time) while cockatiels are a bit more (but not really expensive, either). Budgies come in a veritable rainbow of colors and patterns (I call them 'the little flying jewels of the parrot world') while cockatiels, although having several mutations, are restricted to four colors and the combination of them: black, grey, white and yellow.