We flew last January with the hill-rom vest -- which came with a wheeled duffle bag. Fit just fine in the overhead compartment and we DID fly on a couple very small "puddle jumpers". A friend of mine indicated that they're able to fit the pari compressor AND neb drugs in the case, too. We just opted to keep the nebulizer, neb cups and all the drugs in a separate backpack/messenger bag.
This last trip we didn't have any issues, though one TSA person read the back of the machine and was concerned with warning, which said not to use it around liquid anesthesia or something like that. So she made us wait while her supervisor check the warning, too.