Greetings Mark!
RE: Tow Vehicle Question
Either truck that you mention should work assuming that it was equipped with the intention of such use. The trailer tow ratings for most 3/4 ton trucks vary from 5,500 pounds and 12,000 pounds depending upon how they were optioned while 1 ton trucks typically range from 8,000 to 15,000 pound tow ratings depending upon how they were optioned.
For your situation, the 3/4 ton would probably provide a slightly gentler ride but the 1 ton truck may have more effective brakes. I mention this because you mentioned in your earlier post that there is some question as to whether the trailer brakes are fully functional.
There is a second issue that you will likely need to be prepared to deal with. It is quite possible that your Airstream may be wired to the unique method used by Airstream
(see) that is not compatible with tow vehicles wired to today's industry-standard. My Argosy Minuet was wired to this standard and the backup lights were the only thing that functioned on it when it was first connected to my Suburban (they were wired to the 12-volt charge line terminal); all other lights operated in manners other than intended. The current standard isn't terribly different
(see) , but it does require shifting several wires. It is also possible that you may need to change from a 7-pin round connector to a 7-blade connector to be compatible with a modern tow vehicle.
Good luck with your excursion.
Kevin