Conures are louder, may bite more and generally cuddlier.
Cockatiels tend to be quieter (but they can be noisy, too! just not conure noisy...), not quite as cuddly as a conure (being cuddly can be a bad thing!) and they are dusty birds... which may be an issue for anything with asthma or allergies.
Both species are extremely popular and make excellent companions. If you have a nearby rescue or sanctuary, perhaps you can get to know each a bit better and make a decision. There is also the concept of letting the bird "choose you." If torn between the two, might come down to shopping for candidates and selecting the one most attracted to you.
In either case-, I know we say "cuddly" but you cannot cuddle a bird without sending the wrong impression and triggering hormones, so whatever your decision, no petting anywhere other than the head and nets, no tents/hammocks in the cage and no access to shadowy spaces---these will all create hormonal birds overtime and hormones lead to health and behavior issues.
I've had both cockatiels and conures; currently have a baby conure. Both of my other birds lived good, long lives and both were very bonded to me. The conure seemed more independent and defiant than the cockatiel. Completely different personalities, but both very responsive to attention and both very interactive. I do think the conures are more 'naughty' though! Good luck. I'm sure whichever bird you decide on will be just perfect!