Which is better for a DBA (Swarm); powered subs or unpowered?

I agree with @noble100  that the bass improvement when going from one sub to two is on the order of twice as good.  I stopped at two for now and I am very happy with what I hear but I know the folks with four properly set-up subs mostly report even further improvements.   If you could wait a bit until you can expand your budget the (award winning) swarm system by Audio Kinesis ($3,200 for all) seems bargain priced for what you get and may actually be less expensive than piecing something together and then upgrading.

mc -- thanks for leading me through that photo. Sorry to belabor the point, but I'm still not sure what's going on (if you'd rather do this offline, please let me know how I can DM you). It looks like you have two Dayton amps powering 4 subs, and a powered Talon sub that gets its signal from a bypass through the Daytons (presumably the cable that's half red and half copper colored is going out to that sub); I assume that's because you didn't have another line output available on the Melody. I think one channel (white POC) is going to one Dayton and another (red POC) going to the other. I'm not sure why you use 2 Daytons; does one not have enough power for 4 subs? If so, does that mean you're only powering 2 subs with each Dayton, and feeding them the same (white) channel on both their L and R inputs? Also, it looks to me like the two silver cables with the 3 bands are going from a two channel Melody output to an input on what looks like a CD player -- or is that an output from the CD to a Melody input? Again, sorry for all the questions -- they really should have flunked me out of engineering...

Is it possible to run 4 passive subs off of one amplifier, say like a Crown XLS series? Run in series or parallel?

I don't see why not. It appears the power ratings spec down to a 2 ohm load. If you run two 8 ohm speakers in parallel on each channel, or two 4 ohm speakers in series/parallel per channel you will attain a 4 ohm load.
I use an Acoustat TNT-200 to power my passive sub boxes. I have four 8 ohm speakers per channel in series parallel. A total of 8 subs in the system.

My set up is a bit different in that I triamp using a 3-way active crossover. My two-way ribbon speakers use an external passive crossover and I replaced it with the active. Under 100 Hz to the subs, 100 - 650 Hz to the bass/mid ribbon, and over 650 Hz to the mid/treble ribbon. A push-pull tube amp for the bass/mids and an OTL tube amp for the mid/treble.

Remember, 2 properly positioned subs will provide very good bass at your designated listening position only, but not throughout your entire room.

DBA subs give a time incoherent mess everywhere.

The Dayton has no delay so there is time smearing. What you end up with is a fat, detail-less low end pillow.

For music, two subs correctly positioned relative to the mains for the main listening position are the most realistic.

Of course, if the mains are an incoherent mess spraying sound all over the room, who cares?

Do you not have to adjust the phase of each sub independently? I wouldn’t think that with four subs in different locations, possibly pointing in different directions, that you would want the same phase or even the same volume levels across all of them equally...

I gather that with the dayton amp, you aren’t able to adjust each one independent from the other (?)