Outside of the textbook "hands" answer, which is exactly it in a nutshell when it comes to harshness, I think what you're looking for is the word "severe". What makes one bit more severe than another. The "severity" of a bit would be determined, even by someone with gentle hands, by its construction and its operation. Here's a list of some examples:
1.) Somebody already said the thickness of the mouth. A thinner bar in the mouth hurts the horse's bars more. There's less surface area for the piece to contact with the horse's mouth, so there's more localized pressure. A thicker mouthpiece spreads the pressure of the reins over an slightly expanded surface area. Remember that we're talking about a bit sitting inside a horse's mouth where it is very sensative, so even a little bit of expansion goes a long way.
2.) Again, the twist in a mouthpiece or basically the shape of a mouthpiece in general. The ridges caused by a twisting mouthpiece actually create MORE pressure points across the horse's mouth than a regular snaffle. Instead of having pressure on the bars and tongue, the twisting ridges create a new poking pressure point everywhere they come in contact with the horse's mouth. When used in conjunction with #1 above, you create a severe mouthpiece by coupling a small diameter mouth with a twist, so now you have lots of tiny (but still painful) pressure points AND a small gauge piece of steel on the bars that hurts as well. (twisted wire snaffle). A slow twist is less severe because A.) the metal doesn't twist as much, making less ridges; and B.) the gauge of the mouthpiece is thicker. They're still both more severe than a regular snaffle, though, because of the twist ridges. A broken mouthpiece has more of a nutcracker effect and moves around a horse's mouth, putting pressure on the tongue and bars. A ported, solid mouthpiece lays against the horse's tongue and pulls against the poll, putting pressure on the bars, and the bit tilts and puts pressure on the roof of the mouth. The solid port is actually MORE severe than a snaffle because ports are used in conjunction with shanks for leverage, and leverage is always amplified via the curb strap. Whereas a snaffle has no leverage. However, both were created for a different reason. A curb is not as severe at all when used properly (one hand). A horse, however, does have to be taught how to respond to the curb pressure.
3.) The height of a port. In the ported bits, the heigher the port, the more quickly there will be pressure on the roof of the horse's mouth and on his tongue. A higher port means that you can't tighten the reins as much without sending that bump right up into the roof of his mouth. A higher port is also more narrow, so it's kinda along the same lines as the mouthpiece metal gauge. The more narrow the port, the more localized the poke is on the roof of the mouth = increases the "ouch" factor. A lower port is more stretched out, making it wider so there's more clearance between the tongue and the roof (you can move the reins a bit more without actually engaging so much of the mouthpiece) and the bit doesn't poke so hard in one spot. And a mullen mouth doesn't really poke at all, it just pushes up on the whole roof a little and the horse responds.
4.) Shank shape. The shape of the shanks has a great deal to do with a bit's severity. Grazing curbs have shanks that are tipped back sometimes almost 90 degrees. This means that that when you pull on the reins, the shanks are already in a tipped back position, and unless you're riding with your arm straight up in the air, you're not going to engage them much more than they already are. They won't tip back much farther, so there's less pressure on the mouth because there's less leverage from the shanks. A 7-shank, on the other hand, the shanks curve FORWARD. This means that if you pull on the reins, it actually takes VERY little movement to engage the shanks and pop the mouthpiece up into the horse's mouth. Shape of the shank determines how quickly the mouthpiece will engage the horse's mouth.
5.) Length of the shank. This always goes with #4. Length of shank determines how much pressure will be exerted on the mouth. The length of the shank is determined by where the reins attach in relation to the mouth. The longer the shank, the more pressure pulls down on the poll. A standard straight-shank, low port curb puts about 3 pounds of pressure on the mouth for every 1 pound on the reins. Longer shanks extend that ration, and when used in conjunction with the shape of a shank, you can add a great deal of pressure VERY quickly with very little movement, or you can allow for a great deal of movement with barely any pressure at all. One thing about this, though, is that the curb chain has a lot to do with it, too. Without a curb chain, a leverage bit does nothing. If the chain is too tight, the bit engages more quickly, no matter what and the big squeeze put on the mouth, down from the poll, can be extremely painful. Curb strap/chain too lose doesn't do anything, really.
6.) How the shanks attach. Shanks that are "loosely" connected move around a lot more. They tip and swivel, often ending up under the horse's jaw or sticking out to the side, pushing the purchase (the top part of the bit) into his face. Tom Thumbs do this. What makes a bit like this severe is that is has long, straight shanks AND a broken mouthpiece AND it tips and swivels. All that extra tipping and swivelling movement makes the bit move around in the horse's mouth...i.e. sending him signals. It can be very confusing! Not to mention that the shanks are putting a lot of pressure on the mouth at the same time, PLUS the mouthpiece is broken, which gives it a nutcracker effect. Bits with shanks that move around more and are not as fixed can accidentally cause pain or mixed signals (at least). So you need to have REALLY quiet hands for them. There are semi-fixed shanks which open and close like doors. When the rein is loose, that one side is somewhat disengaged, so there's no pressure. It's nice for helping western horses or curb-bit horses with lateral movement. It kinda just opens a door on one side of their face. It does move, though, so moving the reins around can still send accidental signals to the horse. The completely fixed shanks don't move at all and are the mildest in that respect.
You can build a bit using all different combinations of all that stuff and make a really mild "might as well have nothing in there at all" bit or you can make some really nasty ones. Some bits out there it is clear to me that some dufus decided he didn't want to take the time to work with his horse to understand the problem, so he came up with the biggest, baddest piece of steel he could to try and manhandle the horse into submission. Others I gotta laugh at and scratch my head and say "what were you thinking" because they're so ineffectual or ridiculous and do little to nothing. LOL
Didn't mean to write a book, and I've cut several corners in an attempt to make this as short as I can. Sorry. By all means, fill in the blanks and elaborate.