Would suggest you err on the side of caution and get High rings.
Also depends on the height of your eye line from the stock. If you have a cheek piece that raises your sight line, the higher your rings should/will be. If you have a standard sporter stock, sight line will be lower, hence the lower rings. Medium is really pushing limits with a bigger objective bell. Up to 40mm optics, mediums would cut it.
Extra 4mm = ~5/32” and that is a big difference when space counts.
When it comes to ring height and the space it provides for optics bells.. I live by my carry creed. Better to have it and not need it, than to need it and not have it. Not to force an opinion, but you’d do well to get Warne steel rings. I switched to them a few years ago, and they are all I buy now.