Skiing is more enjoyable, but snowboarding is more stressful to the joints. Jumping around on a board over moguls is just not natural to me. I have only been to a couple of ski resorts. I guess I like Ski Liberty in Pennsylvania the best.
For me, snowboarding wins every time. It's more fun and you can do much more with freestyling and off piste. I do agree with the previous poster though tha it's more stressfull on the joints. If you're looking to try for the first time though I think snowboarding is easier to pick up - you only have to worrk about one board not two :-)
I'm from the UK but my favourite resort by far is Whister in Canada.
For first timers, start with skiing and get the technique and then move on to snowboarding - both have their merits but some resorts are better suited to snowboarding. Favourite skiing resorts.....not in order are: Serre Chevalier, Zermatt, Vail