SIGNIFICANT differences.
A couple of members have written that about ¾ inch in length is the only difference between CDR and full size. I think the savings of 12+ ounces is an important factor. The post-WWII developments of a lightweight pistol for the US military didn't result in a military contract, but Colt's decided to recoup some of the development costs by introducing the Commander for commercial sales in 1949. I think it was one of their great decisions.
Granted, the Commander (CLW) gives up a little velocity and some sight radius to the 5" pistol. It is a pistol for those who carry much but shoot seldom. I think, if I was in a military up-close-and-personal combat unit, or in a police felony apprehension squad, I'd want a full size Government Model, set up JUST so. The full 5-inch gun is also better for bullseye match accuracy, and soaking up recoil during action matches. If, on the other hand, it is just a matter of wanting to be armed for personal protection, or if one's duties are somewhat less rigorous, the CLW is a truly fine sidearm. Compact, about 26 ½ ounces empty, flat, powerful, and (subjectively) points well..
For most of my career I carried a CLW with one spare magazine, and felt reasonably well armed. The mild increase in felt recoil was an acceptable penalty for not having my pants dragged southward by the heavier pistol.
The third choice, the so-called Combat Commander (CC,) 1969, is the worst of both worlds. It has the shorter sight radius and some of the sharper recoil of the [real] Commander, but not the light weight. It is only about 1½ ounces lighter than the Govt Model. However, there's no denying that the CC has been a big seller for Colt's. I think this is because it just LOOKS so good, and it soaks up recoil well. Most who buy the CC, of course, do not carry any pistol on a daily basis. An exception might be certain uniformed peace officers and others who carry openly. Given that a heavy gunbelt helps support the weight, either the CC or Govt Model can be conveniently carried.
AlexGRT, it is your choice and your money, surely. Have you ever carried and shot either of the Commander Models? You're commiting to a significant expense, and you might wish to try 'em out. If you DO change your mind, and it hasn't been too long since you placed your order, you might still be able to order the lightweight frame. If not, a careful choice of a sturdy 1½ inch belt and a good, stiff OWB holster can still make the carry burden acceptable.
Whatever your decision, I wish you the best of luck.
Johnny