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12 Speed Xt on both my bikes. Ultra common (normal!) 10-51 on the trail bike. But on my hardtail I've got the 'racers choice' 10-45 casette as frankly who needs more on a lightweight bike.
I've always run the SGS mech on both, never really paid any attention to the cage length. However the performance has never been great on the smaller casette (not hangers or tuning etc)
Now bent a mech and need to replace - reckon cage length is so critical? I think it puts the guide pulley into a slightly different position too. Perhaps this is the key to the difference in shifting quality between the two casette sizes.
Everyone uses these....

But you rarely see these...

Any first hand experience, Obviously its clear what Shimano say, but its nice to have cross compatability between bikes where I can.
I've run both on a 10-45 and can't say I noticed any difference, so I'd go with the long cage one.
Always ran the short cage on 10-45, never used the long cage. Liked the greater ground clearance offered.
Thinking about it, if you set the chain length in the 10t, so its just off its stop, then the upper pulley wheel will be in the same position. If you set it on the 45t, with the long cage, the upper pulley wheel would be further away, so would need less B tension.
The GS is specifically for 10-45