Players really don't know what they prefer because they know nothing of what map makers have to take into consideration when making a map. Who cares what they prefer :D
And... Blizzard doesn't know how to make good maps. I mean, they COMPLETELY FORGOT to make INVERTED RAMPS in SC1/BW -_-
In most cases, rotational symmetry gives the best use of space on a map, and usually the best thing about it is that it gives the least amount of positional imbalances because everything is equidistant from its other 3 mirrored counterparts on the map.
But I said "in most cases". There are times where other types of symmetry might be preferred. It depends on the concept, really.
Also, rotational symmetry looks the coolest :)
It's my favorite form of symmetry, although it's one of the more difficult forms of symmetry to pull off.
I would say the most difficult types of symmetry is between 3 player maps and Odd-Eye symmetry (from the map Odd-Eye, the Pro map)
It is not better "per se"... No symmetry is. Every symmetry has its own quirks both execution- and gameplay-wise that one needs to observe in order to make a good map.
Fact is that rotational symmetry has a better inbuild "eye candy effect".
That does not mean that axial symetry needs to look boring though, it's really only lack of imagination on the mapper's side that can lead to that impression. With some minor tweaks and twists in symmetry (look what I did in Desertec for example) or by chosing an "odd" symmetry axis (p.e. Gaia... There's really no more recent example I could think of... A shame - but I am already workig on this one, too ;D) you can create an axially symmetric map that looks just as stunning as any rotationally symmetric one.
And it is always possible to opt for hyper-symmetry, of course (i.e. a map that displays both rotational and axial symmetry, p.e. Monty Hall, Arcanoid, Rush Hour...)
In case of 4 player maps axial symmetry means more positional variance (you basically have three different matchups: vertical, horizontal and cross-position or something similar [like Python-layout, which is rotated by 45°]) as opposed to rotational symmetry which only has close-position and cross-position option.
Also, axial symmetry inherently avoids "rotational imbalances" where a player spawning clockwise/counterclockwise has a positional advantage in close-position play.
I think the main reason why axial symmetry is often frowned upon is the "check all symmetry boxes and map away" effect that often leads to bad looking, boring, uninspired and considered "newbish" maps. modified by Freakling
Well Blizz's BW maps sucked...a lot...generally blizz doesnt make that many good maps...although I really like metalopolis...
Well personally I prefer rotational(when properly executed) because it shows the mapper put a crap load of time to get it symmetrical cuz isometry makes it pretty hard to do...I think freakling actually pretty much covered it, rotational can generate imbalances in clockwise/counterclockwise for close position but axial symmetry is just too easy to do, check all boxes and people can crank out maps at like 2 and hour...
The only essential difference in SC2 is that you can disable certain matchups on 3+ player maps, so you basically end up with more of a "variable (2)-map" so to speak if you choose to do so. That does allow for an easy fix for otherwise imbalanced four-player maps by disallowing imbalenced positional setups. (and on the positive side you get a bit more freedom in designing four-player maps)
Have a look at these basic Beltway stats.
Sometimes looking at the number of mirror matches played on a map can help give a basic understanding of the racial balance. The high number of terran vs terran games in this case gives clues.
This only works for proleague maps because teams choose who plays on which map. modified by CardinalAllin
Changing/randomizing start locs via trigger works out rather badly actually...
And the basic idea is that a melee map should be fully playable/functional in melee mode.
And most of all readily available map statisitics are basically worthless. To really judge a map's balance you'd need statistics for all the hundreds of S-class test matches that are played by the pro-teams. As cardinal pointed out: You'll often only realize a maps imbalance by the unequal distribution of mirroi matches on it and often a statistically insigificat number of non-mirror matchups.
Iccup statistics have high game numbers, but player skill are genreally too low and unequal to allow a good judgement on map balance based on them.
The stats for Nemesis are quite a fun example of showing how misleading they can be. Protoss appears to be weak in both PvZ and PvT but the number of mirror matches played on the map show that actually Protoss was powerful.
Admittedly the number of games played is low though.
Stats can give clues, and can help support theories. The more data you have and the more detail it contains the more accurately you can reach useful conclusions. modified by CardinalAllin
And on top of that Balance was never even a main concern on Nemesis - if there's a competition for the most boring possible map layout this one would be definitely an odds-on favourite... (and I am not only talking about looks; standard layout, fully open middle, safe thirds and backdoor nat are as one-dimensional gameplay-wise at it possibly gets... Only the islands are remotely interesting...)
Your average (2)map, both RoV or Odd Eye layout have one symmetry axis. (4)maps like Ground Zero typically have 2. "Hypersymmetric" maps like Arcanoid, Rush Hour or Incidence have (at least) as many symmetry axes as there are players (so Arcanoid has 4, Incidence has 3; these maps are also rotationally symmetric).
Same for rotational symmetry an (n)-player map has an n-fold (or 360°/n) rotational symmetry.