All things being equal if two traditional jiu-jitsu — or other grappling discipline — combatants with similar skills, were involved in a fight, one shorter than the other, would the shorter combatant have an advantage due to having a lower center of gravity, therefore making hip throws, etc easier?
Yes, a shorter person has an advantage for hip throws and shoulder throws because it is easier to get under the opponent's center.
But a taller person has other advantages.
- Longer legs make foot sweeps easier.
- Leg attacks like osoto gari have greater leverage.
- Grappling strategies that crush the opponent from above become available.
Mass definitely provides an advantage, but I would say there is no advantage to shorter or greater height if you control for mass. Fighters naturally develop different techniques based on what is successful for each person, and skill is a much more significant factor.
I find arm reach is not an issue while grappling. If one person can grab, then the other person can grab whatever is doing the grabbing.
On the ground, having short legs may make triangle chokes or controlling from the guard position more difficult. But I think for the vast majority (99%) of people, this is not a significant issue.
With taller opponents, you have the advantage that a smaller horizontal movement will bring their center of gravity beyond their feet. It's also true though that with a taller opponent, you may have issues with reaching designated spots.
With shorter opponents, especially in martial arts like Judo, it's more difficult to get under your opponent for some throws like Hane Goshi. But you have the advantage that reaching them is probably easier than reaching you.
I'm 5'7" and most of the people that I train Judo with do have problems throwing me because of my low center of gravity. My instructor is quite a bit taller than I am, probably over 6', and he'll often use me to demonstrate throws, sweeps, and reaps as I have a Ju Jitsu background and am more comfortable with falling than the others that we train with. While he can throw me, he often comments that he has to adjust his entry angle to get below my center of gravity for the throw.
Now, he's not the only person that has had problems with throwing me. I've had people that were closer to my height, give or take a few inches, and they still had problems. Sweeps and reaps are totally different because of the positioning that you're in to perform the technique.
Being shorter, with a lower center of gravity, can give you an amazing advantage when you're trying to throw someone else, especially if they're taller than you since you're closer to their center of gravity, it's easier to get into position and launch them to the floor. When we learn a new throw/sweep/reap, we'll perform a drill where we first perform the technique on our instructor so he can help correct our positioning by feel. After we run through with him once or twice, he'll step out and the next person in line will step up and we repeat the process until we've had a chance to throw everyone in the class getting a feel for different body types. Due to my height, I'm usually able to step right in to my opponent, pull them into position and perform the technique while keeping my balance where people trying to throw me don't have that luxury.
Being both Tall and Short has it advantages, having a low center of gravity can be an advantage depending on who you roll with or spar.
For me, being tall, I find throwing someone with a lower center of gravity I have to lower myself more (i.e Hip Throw). I would either try a different throw or change my strategy.
For yourself - find what works for you and try things out with people on a variety of sizes.