The Woosh Karoo is a light-weight efficient commuter type of bike. the oxygen S-Cross MTB is a hard-tail MTB, so it's difficult to compare. The S-cross CB would be a closer comparison. You get hydraulic brakes, reasonable suspension forks and a cassette motor on the Oxygen MTB, which are the main contribution to the price difference.
I've ridden the Oxygen, as they have them at my local ebike shop. It's very fast (derestricted) and sure-footed. It really inspires you with confidence when you ride it. It would be great for light trails and bumpy roads as well as making it as a fast comfy commuter.
I haven't had a chance to ride the Woosh Karoo yet, but i'm sure that it's a good bike too. I'd upgrade the brakes to hydraulics if there's money in the budget. That gives you set-and forget reliable brakes. I can imagine that it's a little more efficient than the Oxygen regarding battery usage, and on the downside, not as comfortable when the road gets bumpy. Maybe someone can send you a PM about derestriction if that's important to you. At £900 it makes it's pretty good value.