Thanks for your response. I'm not sure about fluid specs, as companies tend to conflate marketing claims with specs. The John Deere 1025R is fairly new so I've only done one transmission fluid change on it so far. I was in a hurry so didn't research options and just spent the $$$ on John Deere Hy-Gard oil so that's what's in the Deere. John Deere seems very careful to avoid any statements about what Hy-Gard actually is, preferring to make us think it's made with magic pixie dust from fairies who only work for John Deere.
The Kubota is due for a hydraulic filter change and top up. I don't remember what went in there last time, but this time my wife bought a 20L pail of Premium UDT and that's what's about to go in there.
I did find
https://jdparts.deere.com/partsmkt/unsecured/document/english/featbene/hygardsalesbrochure.pdf which states that according to John Deere, Hygard can be used where UDT is specified. So presumably both tractors could use either Hygard or Super UDT just fine. Not sure whether it's OK to mix them (I'd tend to think yes but I'm not a chemical engineer) but I suppose I could flush the Deere and put Super UDT in that too.
Thoughts from anyone knowledgeable on having those two oils in the separate tractors, mixing through the shared trailer, vs. flushing the Deere and putting Kubota Premium UDT in that?