I agree, the cage you have Henry in right now is far too small for a Budgie, they are no different than any other species of parrot. They have the intelligence of a 2-3 year old child, they need tons of exercise every day, they need a low-fat, healthy, varied diet, they'll get Bumblefoot from sitting in a little cage on the dowel/perfectly-round perch, and they need tons of interaction every single day. Same as a Parrotlet, same as a Sun Conure, same as a Cockatoo...And understanding that, you should see why Henry's cage is far too small right now.
I always go by the rule of "Buy the largest cage you can afford and you have space for"; with Budgies you do need to make sure that the spacing between the bars is close enough that he can't fit through them...Other than that, you want the largest cage you can get him, and "Flight Cages" are always a great option. Amazon.com has a very nice, large Flight-Cage for $99, and a double-version of it for a bit more...The single-version would be great for a Budgie or two.
****Here's something that EVERYONE should realize: Pretty-much EVERY bird cage you see in any pet stores that is labeled as being a "Budgie or Parakeet Cage" is WAY TOO SMALL for a Budgie/Parakeet. I mean they are so small they are at the point of being abusive/neglectful...In fact, at Petco, the 2 cages they sell that are meant to be for "Budgies/Parakeets" are like putting them into a trap or something, and the same goes for their cages supposed to be for "Cockatiels", in fact they're worse because Cockatiels are much larger than Budgies/Parakeets, but those cages labeled for them are not! So the lesson is never buy a bird cage because the box says it's for the species of parrot you have, because 9 times out of 10 it will be way too small...