Welcome to the forum!
Glad you could be here.
My mother used to raise both cockatiels and budgies, and I currently own a cockatiel. In fact, she's standing on my laptop as I am typing this.
Anyways, both birds are small, with big personalities. Budgies are more energetic and playful, and they have more of the attitude, than cockatiels, who tend to be more mellow, and in certain cases, more cuddly.
Budgies are also great talkers, and can mimic any word or phrase, with enough practice. Cockatiels can talk, but they're more commonly known to whistle and learn songs you whistle to them.
Budgies are often viewed as the ideal "first bird", but I don't really believe there is any bird out there that would match the ideal standards as a "first bird". Both cockatiels and budgies can do well. Budgies, because their smaller size makes them out to be slightly less maintenence, and cockatiels, because of their mainly easygoing personality.
So it's really up to what you want in a bird. If you want an energetic bird that can tend to have a bit of an attitude, but is very smart and can quite a few words and phrases, go with the budgie.
If you want an easygoing bird that would love to be pet (not saying a budgie wouldn't like being pet, since I've seen some very cuddly ones), but can also be a playful goofball, (and is also very smart) and can learn to sing some of your favorite songs, go with the cockatiel (keep in mind that the males are usually the singers. This also goes with budgies and talking).