In general I'd say it is easier to get the basics of skiing than snowboarding. However everyone I know learnt by doing ski/board school on holiday where you have a few hours each day. Are your half-hour lessons private or part of a group? If it's in a group then I'd be concerned about how much you'd actually cover in half an hour, and suggest at least an hour instead. Even 1-2-1 it's not a lot of time to learn a technique & practice it.
When I learnt to ski, we had a week of ski school, and were able to stay upright, stop, turn etc on day one, albeit in a very rudimentary way, and went on real runs (big wide open ones) on day 3.
Snowboarding is a different kettle of fish. It's not uncommon to do a week's holiday and not leave the nursery slope! Some people do just "get it" but they're a minority. My SIL & her DH had lessons & by the end of the week he was able to do a run, slowly & with a few falls. She still could barely go a few metres without falling.
I picked boarding up relatively quickly, but that was largely because I could already ski & some of the theory is the same - e.g. How you hold your weight, leaning down the mountain (feels very un-natural and scary!) etc Even so, it was at least day 4 before I could go on a real run with DH and his friends. And my muscles were screaming!
I've never done either on the carpet treadmill thingy. DH has had a private snowboard lesson on one to perfect his technique (he's pretty good already) and he says it felt quite weird, and not like snow. It hurts a hell of a lot more when you fall, and also doesn't prepare you for the change in conditions (soft snow, slush, ice etc). Do you have a place near you with the "real" snow? Tamworth, MK, Leeds have them from memory, but not sure down south. That would definitely be better than the carpet thing.
Also, where are you going? Some resorts are significantly better for boarding than others. Where there's flattish bits between runs, on skis you can just schuss along with your poles, but on a board you'd have to take it off and walk which is v annoying! On skis you don't need much of a slope to push off and practice turns etc, but on a board you need a fair degree of a slope just to move. Worth looking what the lifts are like too as using a drag-lift on a board is VERY hard, even for those who have done it for years. Chairlifts are tricky too, and I've found in some resorts (particularly in France) they can be quite strict about it when you're very obviously a beginner who can't use the lift properly as it holds other people up cos they have to stop the lift for you to get off.
Whichever you do, I'd definitely start doing some squats before you go as your thighs will be aching.
Good luck!