There's lots of info here on the forum regarding these sorts of topics, I linked to a couple to get you started below. Spend some time in the "search" section to gather info from some older threads. Here are a couple of my initial thoughts for now, I'm sure others will chime in.
If the 60's trailer were well maintained or restored, there's not really any "big red flag" reason that immediately comes to mind why it wouldn't be as conducive to full-time use as a 70's trailer. Some parks have issues with "old trailers", but if they don't want me there, I certainly wouldn't want to stay there anyway! One thing, as far as durability goes is, the 60's trailers cabinets have more solid wood or veneered plywood vs vinyl or tambour in the 70's. The wood panel type doors, in my opinion, are more durable than the tambour.
Another thing you would have to contend with that may help make your choice, is that the 60's trailers don't have grey water tanks, unless they were retrofit during restoration. If you intend on full-timing in RV parks with full hook-ups then it's not an issue. If you would be boondocking you would have to deal with an external tank or "blue belly"
daily. It's not a big deal for a couple of days...but full-timing it would get old real quick.
The layout/length would be a bigger issue than the age. I know of some folks who full-time for 6 months at a time in a 19-footer like ours...but for me an Overlander, at 26/27' would be the shortest I would attempt to live in full-time and an Ambassador or Sovereign
would be even better.
You don't say where you are located (in your profile) to have an idea of the climate you would be in. If you would be dealing with severe winter weather, you may want to reconsider the whole idea. Airstreams really aren't good in long snowy winter living
That should be a good headstart on some things to think about ~ beyond that...it's a personal choice.