I have Crimson Trace grips on three handguns, and would not consider buying a handgun that Crimson Trace did not make a set for. You may consider me sold on them. I have the LG305 Crimson Trace grips on my 637. When I bought the revolver eight years ago, they were the only model available. As someone pointed out, there are now three models. Each has its own set of characteristics. The primary advantage of the LG105 set is price. The second advantage is enhanced concealability due to its shortness. It has several disadvantages. First it is made of hard polymer and does not cover the backstrap, so it will kick like a mule. Second, I at least find that, due to the shortness of the 105 grip, my pinky has no place to go, which adds to the controllability problems. The LG305 grips (that I have) has two advantages. First, it is made of rubber and covers the backstrap, thus providing some (but not all that much) protection from recoil. Second, it is long enough to provide room for my pinky. On the minus side, its full length detracts somewhat from concealed pocket carry for those who wear tight-fitting trousers (but not for those who wear slacks as I do). It also is a third more expensive than the 105 set. The third model is the LG405. Its primary feature is a sort of shock absorber high up on the backstrap, right where I tend to create, and pop, a blister if I don't put a bandaid on the web of my hand. It costs as much as the 305s, and also has no place for my pinky.
Since you haven't yet fired your 637 Airweight, you have an experience coming. Many, including me, find it punishing to shoot more than twenty rounds at a session. Then there is going to be the shock of watching that red dot jerk all over the target. That is YOU doing it, not the laser. For the first time, you will see just how bad you are. For many, that is too much, so they quit and thereafter have nothing good to say about laser sights. I was discouraged at first, but stuck with it. I now have the pleasure of watching a black hole appear in the target where the red dot used to be. I still practice with iron sights as well, but in a home/self defense situation (which is what I practice for) I would use the lasers.
Cordially, Jack