Hmmm. Well, I'm not faster with the loading gate on my Rossi, that's all I know. I've shorted the tube spring and smoothed the edges of the gate. And there's the counting or else there's that little hitch at the end when I can't get another round in, and maybe it tosses it back at me to let me know that. Sometimes the the cartridge doesn't want to go into the Rossi's magazine if it's angled a little bit wrong.
But despite me liking the tube better at the range, I can definitely expound on its drawbacks as I see them. They fall into two categories: tactical considerations away from the range and various concerns about the muzzle direction while loading at the range.
The tactical drawbacks are obvious. Enough said about that.
I can't speak for the rifle caliber lever guns, nor the Henry lever action shotguns (footnote), but if you know the Henry Big Boys, you will close the action to load it, and that means futzing about near the muzzle with the bolt closed. Best to make a strict religion out of lowering the hammer before pulling the tube. You need a gravity assist for the rounds to slide down the tube, so the rifle will held at an angle and might be pointed above the berm, or at least flirting with the top of it, while you're loading. That wouldn't be as big an issue if the action didn't need to be closed. There are ways of dealing with this if the range requires it, but the point is that it's a hassle not present with a loading gate.
Finally, sometimes the loading tube will hang up a little on the rims of cartridges as you lower it. Although this is not a problem in and of itself (you just wiggle it a little to get past the obstruction), if you're trying too hard to avoid muzzling your hand to the point where you don't have a good grip on it, even a minor hitch could result in you launching your tube downrange.
(footnote) It may be safe to load the Henry 410's with the action open. IIRC, the blocking tab is long enough on these models that there is actually a hole cut in the receiver for it when the bolt is closed. It seems possible that this blocking tab, unlike the tabs on the Big Boys, is long enough to block the magazine tube even if the lifter falls to its most extreme "up" position.