Well they are about equally bad, in being hard on the horse.
You are pounding on the hard stuff, lots of shock going up the legs. You are taking chances of straining the horse in the fetlock deep stuff. The fatigued horse is most likely to hurt themselves in deeper going, and deep going fatigues horse muscle quickly.
Is there any chance of working with the barn manager to get the hard ring worked up a little, sand added or the deep ring watered regularly so it is not so deep?
The no footing place is a big no on getting footing. It's going to be quite costly and since the owner doesn't really use it, he's not super anxious to spend a bunch on something he won't use. And rightfully so since it would be something he almost never used.
The deep footing could be worked on I'm sure. Thankfully I live in Texas where it rains it seems daily! LOL! I would even be open to watering it myself I guess. I can always find chores to keep me busy while the sprinkler goes.
Excessively deep footing can cause soft tissue injuries(suspensory ligament, flexor tendon,etc ). Hard footing would be more likely to cause injury if the horse was being asked to do a lot of circles, speed, turns etc.And those kind of injuries would be more likely in the foot lower (collateral ligaments, coffin joint, impar ligament )Therefore which is worse depends on what you are doing with the horse.
Just had a thought. Could the bad footing place do some bedding spreading on the ring area? While we northerners see that practice making muck on solid base, muck mixed with hard dirt could be exactly what the ring needs.
Not sure what bedding he uses, sawdust, shavings types would probably be best for holding moisture, taking longer to break down to dirt.
If he has a disc, the ring could be dragged to cut dirt, break the hard top open, after the initial layer of spreading, so bedding is mixed a bit with the dirt. Ride on it, use the ring. Then continue the spreading to cover the whole ring area, work dirt with the disc, but not digging deeply. You just want the top 3" or so of dirt "disturbed" so it can mix a bit better. Then you could probably do a regular dragging to smooth it out some, mix dirt and bedding for riding on.
Then you just ride it, see if it seems to be improving any for you. You can add more bedding, disc and drag again to mix it in, if dirt gets hard.
The woody fibers will hold moisture and help keep the clay from packing so badly. Not sure how much bedding addition will work best for you and this dirt. You want to end up with a cushy layer about 2 inches deep, with firm footing under for grip to the horse. Horse does best with this kind of layering, gives him cushion, the grip lets him trust his feet in movement at all speeds.
Know that the woody fibers will break down, turn to dirt over time. Each location is different, depending on how much use ring gets, water from the sky, sunshine. Part of natural process! So adding will be needed in the future, ring may even be muddy, slippery on wet days with this bedding addition.
Dragging the ring to loosen top layers, mix bedding in, will help keep the cushion layer, softer, light for the horse.
Straw bedding could do a similar job for you, but straw breaks down lots faster, may be dusty or slippery footing if not worked down into dirt. Straw is slippery just by itself. With straw bedding mix, ring would need to be more frequently added to so it stays cushiony.
All the above is supposing the BO has machinery to do this with.
I had this issue at a previous barn. It was either ride outside the ring on ground that gets very hard, very quickly in the summer or in a very deep ring. Before I ever even started to break my young horse, I had my vet look at the ring and he said it was just too deep, that I was better off outside the ring on the hard ground. He said firmer is always better than too deep. Of course, that was knowing that this was a horse just starting, so there would be no galloping and jumping.
I hate, hate, hate bad footing. Ideally I'd choose "neither" but if the place with deeper footing was workable and willing to perhaps remove some, I'd choose deep and fixable over rock-hard with no chance of improvement.
Yeah and since we're jumping a lot I worry about the impact on his joints. Of course ligament wouldn't be great either. But the good news is that we can water it down or wait for rain to do anything big!