We were out in the Cairngorms with snow shoes yesterday and I would not have liked to not have had them, due to the deep drifts of fresh snow over heather and whiteout conditions for skiing.
However they are ungainly and more tiring than using existing compacted trails.
Once the season gets underway and the snow consolidates I'll rarely use them. I prefer to use sensible route choice, skis or follows other groups tracks!
From the climbing point of view the one advantage is you can use your normal climbing boots on mixed routes rather than ski boots.
Having said that, if you really need to use snowshoes due to the depth of snow, the avalanche risk will likely be high and climbing is unlikely to be that great!