I know, but I feel it is much nicer that they are able to fly around whenever they want. I know that your birds were let out for a very long time, and they were happy. But I've talked to lots of other people before (kids at school etc.) that have caged parrots, and some don't get let out every day, or if they do it is only for an hour or sometimes not even that. So as long as you are extremely committed to letting it out every day, for a legnthly peroid of time, then a cage is OK, but I feel it is much less hassle keeping them in an aviary.
It's like fish; you can keep some larger fish in smaller tanks, even though a bigger tank is a better option, and the fish will OK, as long as you keep on top of the water quality, which = lots water changes, minimal feeding, more work, and it is really easier to get a bigger tank. So do you sort of have an idea of what I mean?
Maybe finches might be a better option as opposed to parrots - you can have a rather large cage, or a small aviary, which will suit them fine since they are such a small bird. If you make the cage yourself it costs less than the stuff in petshops, plus you can build it to your own needs. I know you can't interact with finches like you can with parrots, but they are still a very cool little bird.