I think it probably depends on the area you hunt and what is around you. Now if you are hunting a field edge a gun would give you definite advantage due to range. If you are hunting thick cover in the woods, ranges will be close to the same, you may get an extra 10 or 20 yards with the gun, if a shot presents itself.
The thing is just because a weapon offers more range doesn't mean you have to use it. Who says you can't wait until a deer gets close with a gun? I have shot them at 20 yards with a shotgun before. It all boils down to what you want to do.
What I know in my area is during the early season (pre rut) it is much easier to get close to deer and pattern them. Once the rut starts they get a little unpredictable and you have to change your tactics. And during gun season unless you hunt an area with very little pressure it just becomes a crap shoot sometimes.
Another thing I have noticed if the deer are close they are no easier to kill with a gun than a bow. I hate that argument, you see it mostly with crossbow arguments though. For me that fact that you have to draw the bow means nothing. Regardless of what weapon you choose you have to bring it up, aim it and hold until you are ready to shoot. All of which will get you busted if the deer sees you, doesn't matter what weapon you are shooting. I actually think a crossbow is the hardest because they are so cumbersome to use. I have never hunted with one though, just played with them in the back yard. But I handled them enough to know I wouldn't want one in a tree.
If you can't lift your bow, aim and draw in a fluid motion you have too much bow and this is no ones fault but your own. And I can actually hold steady longer with a modern compound than I can a rifle (especially my heavy ass H&R ultra

).
I will concede though that I am not half the hunter some of you are, I'm just not that passionate about it sometimes. I am a decent marksman and love weapons of all sorts, but my hunting skills could use some work. However as long as I'm not too picky and have a decent spot to hunt I don't have much trouble taking deer every year. I don't seem to have the buck fever problem either. I have anxiety issues anyway, so I am fairly calm when I see deer. I fall apart after I shoot them. The absolute hardest thing about hunting for me is not jumping out of the stand right after I shoot a deer. That wait kills me (not as much the deer though I guess

).
I don't rifle hunt either, shotgun an muzzle loader only where I live.
I will say that if you hunt an area that offers more range a gun is an advantage. With an inline and a scope if I can see it with the naked eye I can pretty much kill it ( I don't see too far anymore, I'm talking with in a 100 yards or so).
But in the thick cover of the woods I think I would rather have my bow, or at the most a smooth bore shotgun that was easy to handle.
Something else to consider is that here in MI bow season lasts twice as long as gun season.
My opinions and nothing more.
Paul