I own exactly the two you are describing (albeit in 9mm) -- the new-ish Competition model with the blue grips and the latest-issue Lightweight Commander. You'll probably hate me for this, but I got both, specifically because I had the same questions you had.
First, let's agree on the differences other than barrel length and sight radius (and make note, again, that I have the Lightweight Commander, not the Combat):
• Weight. Big difference here, but the significance can go either way. The full-size is more stable, arguably, but it feels heavy to me after a hundred rounds or so. On the other hand, the Lightweight Commander isn't especially light compared to, say, a Glock 17, and I think its weight is perfectly reasonable.
• Sights. The Competition pistol has fiber-optic sights that I love (I use the red), and it's a big advantage (for my eyes, anyway). The white three-dots on the Commander are fine, but I want to upgrade them.
• Frame. Most people seem to overlook this, but the aluminum-alloy Lightweight Commander has serrations on the "front strap" while the steel Competition model has a smooth surface on the front of the grip. Take your pick. I like the serrations. (I don't know if the Combat Commander has serrations, but, being steel, I suspect it does not.)
• Barrel. The Competition model has the "National Match" barrel, but, I dunno ... both guns are more accurate than I am.
As you probably know already, everything else that makes these 1911s "modern" is the same: Series 80 firing mechanism, skeletonized trigger, undercut trigger guard, plastic mainspring housing, palm-swell grip safety, extended thumb safety, extended beavertail. These are pretty damn cool guns, and they are fun to shoot. (Especially in 9mm ... I'm tellin' ya, crazy fun.)
RECOMMENDATION 1: If I had to pick one and only one, it would be a Lightweight Commander with a fiber-optic sight upgrade.
RECOMMENDATION 2: A Competition model in .45 and Lightweight Commander in 9mm with upgraded sights.
Have fun. You're gonna like those things.