"If we split up the current player population (~450) into 3 150 player maps, what is to keep the players in each of those maps from congregating into 3 50 plane furballs? "
A good question, and one which the the answer isn't very apparent to until you see BOTH systems in action. This is something that'd be easier to witness in action or explain in person, than explain on an internet BB. However, since you seem genuinely interested, I'll do my best.
In the case of the 150 player map, in order to have a 50-plane furball you need fully 1/3 of the entire map's player base in one area. On a 450-player map, you only need 1/9 of the player base in a fight to create such a fight. So just from that standpoint alone it's more likely that such fights will develop in a more populated map.
But there's more to it than just numbers. Most players tend to go where the action is. The result of this tendency is the total number of fights does NOT increase proportionally as you increase player base; more players will make the available fights more crowded instead. I've noticed that when there's 450 players online in AH, there's only slightly more "hot spots" than there are 200 online. The difference is instead of around 20 guys fighting for a base with maybe around 12 in the middle at any given time, you end up with maybe 60 guys fighting for a base and 30-40 slugging out in the middle, with the associated lag and warps.
As a result, increasing map size does not create enough extra fights and lead to more even distrubtion of the player base; instead you just end up with literally hundreds of miles of wasted space.
In a small, 150-player map (or any other smaller number, up to about 200 IMO), the fights that develop will tend to remain smaller in scale and hence lag and such won't be as much of a problem. There will also be, proportionally, less empty area in a small map than a large one.
Another important issue is scaling the terrain to your player base. Base distances affect the density of battles, more than number of bases or map size does. One problem with the AH arenas is the base distances; these distances on a map like NDISLES are fine for 300 players but IMO a bit too far for 150-200, and considerably too far for when there's -100 online. When there's 400+, they're actually too CLOSE together, further increasing the density of the big fights. While it may be possible to shut down "fringe" bases during off-peak hours to cope with milkrunning on the PIZZA map (as HiTech suggested doing), it is NOT possible for the base distances to constantly change. An advantage of having a smaller max player base is you can better scale your terrain for the number of people who will use it.
You probably COULD scale a terrain to operate well with 500 players and no overcrowding, but it'd have two big problems. First, flight times to and from the fights would have to be very long (to keep density down), which will alienate most players. Second, during off-peak hours the bases would be so far apart as to prohibit good sustained fights from developing at all--I cannot think of a way to enforce a "MINIMUM" player population, only a MAX.
As I said, there IS more than one solution to this problem; multiple arenas is NOT the only way to go. You can, for example, create "zones" inside the single arena with a max population limit (AW actually had such zones although they rarely came into effect because the players usually sorted themselves out naturally); such zones would by nature prevent the population from congregating all in a few areas. A "zone" works by preventing people from taking off from bases inside a full "zone"--obviously the flaw is if zones are too full for too long, players will start to get angry. They're a good backup system to prevent local overcroeding, but IMO not a permanent fix.
I am a proponent of multiple arenas instead of the other solutions because of the obvious advantage of having 3 or 4 arenas versus 1 in that you can do different things with the different arenas; as long as the basic setups remain similar each will draw players. Variety is a GOOD thing

Does this help?
J_A_B