and I think Aragorn is easily the next best choice.
Okay, we've got 8 to choose from, but Legolas is already my top choice, so that leaves us with 7. I think we can eliminate Samwise and Éowyn. While both have some great moments (and I consider Sam to be one of the key heroes of the trilogy), neither of them are trained warriors. I would not fancy their chances against the rest of the field. So that's two more down, 5 to choose from. Next, which of the other three humans are we going to put above Aragorn? Aragorn is simply a better version of Boromir, Éomer or Faramir in just about every way. He is one of the primary heroes of the film. I could break it down further, but looking at the voting results, it seems like none of those three are being considered above him. So three more down, which leaves us with Gimli versus Aragorn, which we'll touch on below...
from what I can see he's pretty average
How did you watch those films and somehow manage to leave with the opinion that Aragorn is average? He is very far from average. He is straight up one of the very best fighters, defeating many enemies throughout the trilogy. He is also very smart and a natural leader (despite not wanting to be king in the movies). He's a great tracker. He's resilient. etc. etc.
So? It's not like the Dwarfs are some unstoppable force in LOTR, let alone in the Hobbit (where many of the party are kind of goofy). The human race in LOTR is pretty powerful, with powerful cities, armies and major victories. Outside of Gimli, the Dwarfs are either hiding away or dead. The humans, despite needing help, do step up and are instrumental in winning the day.
Gimli's age, experience or natural toughness
Gimili is older, but that doesn't necessarily make him better, especially in terms of combat. There is a reason why there are more UFC champions in their 20's and 30's than in their 40's or beyond. As for experience, I'd have to leave that to someone more versed in the Tolkien world. Gimli has had more years of experience, but I'm not sure about the variety of experience. Outside of the films, what has each one done, seen and taken part in? I genuinely do not know, so I can't compare their level of experience. However, for all his experience, Gimli is usually just the tag along; while Aragorn and Legolas lead the way (in the absence of Gandalf of course).
As for toughness, sure that is a fair point in favour of Gimli. However, Aragorn is superior in terms of agility, speed, endurance, reach, leadership qualities and intelligence. A pretty good trade.
and Gimli also wears finely-crafted Dwarf armour where Aragorn does not
I'm not sure how great that disparity in quality is in the LOTR universe. From the films, at least visually, they don't seem that drastically different from one another. It is the Elven kit that is continually portrayed to be the best gear.
And there's no long-distance running involved so he can't beat Gimli that way
There could be situations where long distance running might come in handy. The scenario begins at random starting positions. I can imagine scenarios where it might be advantageous to run to a superior position or out of a really poor one. Remember it is 6 vs 2 + you, an advantageous position is likely a necessity for any chance of survival. Also, if you are separated from the pack with either Aragorn or Gimli trying to chase you down, you might be able to outrun Gimli (depending on your fitness and athletic level). Aragorn as your enemy, would be far more dangerous in that situation.
Overall though, and let's break the fourth wall, Aragorn is one of the central heroic characters of the saga while Gimli is the comedic relief. We get a good laugh out of his goofy actions, decisions and shortcomings (pun intended). He's a great character, but if my life is on the line, the "funny character" is hardly going to be my first (or second) choice. Going by the movies, visually, Aragorn in my eye comes off as the superior combatant. He is also a better strategist and leader. I'm not trying to sell Gimli short

, he does prove to be a very good fighter and a valiant ally, but Aragorn is the better choice across nearly every metric that matters.