Current arena champion here.
I much prefer random map over the other maps. It's one of the greatest things about this BGA implementation, because you don't get to randomize maps like this in an offline/tabletop game of Gaia.
The "weird" configurations created by Random Map give these games much more strategic depth than other map types. It allows for some truly creative (and strong) openings, nuanced faction bidding, and even End Game objective dynamics. Examples:
1. Three transdims in a row? That middle transdim now becomes a keystone planet for Baltaks or Itars/Terrans who want to avoid early Nav. And in the Lost Fleet, it's now possible to gaiaform all 3 purples in the same round without Nav!
2. A cluster of 1-dig planets next to your home planet? Allows you to play without Nav, and becomes a lucrative area for Lantids as well.
3. In general, random map allows for more openings without Nav due to the unorthodox planet positions. If you can spot these crazy openings for a particular faction that otherwise looks weak, that gives you an advantage in auction bidding. So you're rewarded for seeing things your opponents don't. That's strategic depth.
4. An entire sector of mostly empty space, with just a couple of transdims? If the End Game scoring is Most Sectors, it becomes an early fight for those two purples, may even tempt a Geoden player to research gaia1 for it.
Now let's look at Variable map. I've played plenty of these and others can chime in as well. Notice how early Nav2 is almost a given on Variable Map? It's because of how hard it is to reach desirable planets without Nav2 on Variable Map. The limitation on home planet positioning imposed by Variable Map forces players into cookie-cutter openings like Nav2 mine sprees, because it's too often the most optimal. It's not surprising to see a 4p game where by Round 2, three or four players are already on Nav2. From there, these games quickly escalate to a fight for Nav 5 among the players. That's very limiting in terms of strategy, to be forced into a particular path, and then have to double down on it because losing Nav5 hurts more now that you've invested so much in the track. Imagine if those two early valuable research steps on Nav could be spent on the 5 other tracks instead, we'd see players attempt a more diverse set of early game strategies.