In MT where I spend most of my time chasing elk you can hunt with both weapons each season with the same tag. I used to spend a lot more time hunting back when I was in school and didn't have to work for a living.
Now I'm lucky to get in one hunt and usually alternate between rifle and archery seasons each year.
I spent probalby equal time with bow in hand as rifle each season, I'm guessing 8-10 each year? Probably more in rifle season. Hunted out of my backpack in bow season most times but sometimes with horses and usually packed in with horses, or hiked in dayly during rifle season. As far as 'dificulty'... I think during the rut you'll see 3-4 times as many elk, and see many more nice bulls, but the odds of getting one in range is pretty low. I figue on getting maybe 2-3 chances at killing an elk in a bow season where all the stars where lined up for a kill. The weather is generally nice and more of a picnic than a hunt. You can cover lots of ground with no snow, but it makes for tough stalking conditions at times when its crispy. I'm more intersted in the 'hunt' than the kill and much more perfer to chase elk in bow season even though odds of sucess are generally much lower.
Rifle hunting can also be just as dificult for difrent reasons, There are far more hunters in the woods, the elk have shut up, and have split into small bunches. Azz deep snow makes for tough going, but also makes the animals more visible and makes them feed longer during shooting light. Success seems to hinge heavily on weather or has in my experience. I have however killed 75% of my elk within the first couple hours of opening day of rifle season... so I'm not sure if it makes it hard or easy? The other 25% were very tough to bag however...
IMO I'd say that killing an elk in bow season is more of a challenge, but the hunting is much 'easier'. I really enjoy both types of hunts and am glad that we have the option. I've recently become addicted to muzzle loader hunting, kind of the best of both worlds. Have to get in close but still get to put the 'smack down'.