A lot is going to depend on terrain, too.
I am not skilled enough yet on skis to feel comfortable on steep downhills (and what looks steep to me is probably a minor bump to better skiers).
On snowshoes, however, I can go pretty much anywhere, in any terrain, with trees or not, and feel comfortable and make good progress. I can zip downhill in them, surfing on the tails, and a pretty decent clip too.
I don't recommend getting the biggest snowshoes that can carry your weight - I'd say there's even an argument for getting the smallest that can carry your weight. But, there are other factors too, like type of snow and whether you'll be on steep traverses.
My favorite snowshoes are probably the Northern Lites, with some Crescent Moon Magnesium 9s or MSR Evo Denalis tied for second place. The former are light and work in lots of different conditions, but they don't have as aggressive a set of crampons (= better traction in compacted snow and ice) as the latter two.
Main thing is to get out and try it; see what works for you. REI and other stores rent snowshoes, and that can be a good way to start out just as it is with skis.