So I've made some posts related to combat speed, and mapped combat vs. mapless combat.
Here are what I perceive as the upsides and downsides of both:
Agreement & Clarity. Everyone knows where everyone is. It's clear who is facing where, who is in which hex, and everyone's relative position.
Reach: Weapons with a superior (or inferior) reach matter more on a map.
Defenses: By the GURPS rule books, you don't get Retreat without tactical combat, so effectively your defenses are not as good.
It looks cool. The visual impact of minis on a map is tremendous. Players take pictures of the session not only to record it but because it's fun to see well-set up minis in action.
Time. It takes longer. If only the setup time and cleanup time, fights which require a map and minis will take longer.
Resources: You need a map, terrain, markers, minis, and status markers.
Speed. Turns tend to take longer with a map, because of the issues of tactical precision, below.
Double Edged Swords:
Tactical Precision. Your ability to leverage your position, your enemy's facing, you friends positions, your movement score, and everything else is improved with a map. So is the cost of doing this poorly. Having a map means your decision a couple seconds ago to step or turn or whatever can come back to bite you. Your ability to move around can get you into trouble where you can't get help. Moving may shore up your position or undermine it. You get no benefit of the doubt on where you are or how you were facing.
No Fudging. That is, you can't really just rule people can or can't attack. You can't wing mapped elements. You get locked into a precise set of positions and it's harder to just fast forward to victory or defeat once it's become obvious you are winning or losing without any consequence to tactical decisions made in the process.
Mobility: Movement matters, and slow fighters slog around and speedy ones can take advantage.
Overall, I feel like mapped combat giveth on one hand (more precision, everyone is clear where they are, you can use Reach, Retreat, and Facing to your advantage) and taketh away on the other (you are precisely where you are, positioning matters, and you can have Reach, Retreat, and Facing turned against you.) It costs time, however, and speed of play.
Sometimes you must go mapless, because of real-world concerns (lack of minis, lack of maps, lack of time, fights too big and spread out for minis, etc.)
Speed. Less to decide, so you can decide faster. Many more actions are "attack the guy close to me" and just caring who or what is in front of you, to your left, and to your right.
Easier. There is much less to know for the players. You only need to know the combat basics to get through.
Time. Less setup, no cleanup.
More confusing. It's harder to track where everyone is, and it's almost certain people won't have a very solid idea of where all of the combatants are. The larger the combat, the more this becomes an issue.
Spells. Spell casting penalties are tricky without a map. At -1 per yard, you really need to know precisely how far or close you are. You can overcome this with range band-like default penalties, but you can't get around them ("I step forward in the -5 band so I'm at -4!" = Nope.)
Double Edged Swords:
Tactical Precision. See Mapped, above. Basically, you can't really use your tactical understanding of hex map fighting to leverage your Reach, your Facing, and your Move and exploit those of the enemy. And the opposite - you don't suffer any of the major consequences of them.
Mobility. You are not rewarded for higher mobility because there isn't anywhere to move around. You aren't punished for being a Move 3 tank, either, though.
Overall, you have to trust the GM and just take some answers as answers. This isn't to say mapped combat is for players who don't trust the GM (in that case, don't play with each other, period.) It just means if you thought you were set up to hit the guy attacking your buddy and the GM says, no, you can't get to him - you can't get to him. Ultimately it's how the GM pictures it that matters, and you can't argue it very effectively. For players who don't like to cede any information about a situation
Really, mapless combat is just "adventuring as normal" but with violence. Like opening a door or a chest, or when a bar fight happens, or whatever - it's mapless but has consequences. You have to accept some fuzziness and assumption. If you try to have the best of both worlds, you actually end up with some of the pros but all of the cons of both styles. And personally I think no fight or PC has been lost directly due to lack of a map. I've seen a number of people killed make-a-new-guy dead in tactical combat. And as for speed of decisions, I don't see anyone really making better ones with more time spent.
Short version: without a map, you give up the benefits (but also the consequences) of tactical combat elements. Things go faster but you have to be willing to accept the downsides of vagueness to do it. Both options have elements that affect the combats positively and negatively.
Did I miss anything?