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


I want to start building a swarm (starting with 2 subs), on a budget.  Starting with $1000, am I better off buying two used powered subs, three less expensive used powered subs, or a subwoofer amp (eg Dayton SA1000) and two (less expensive) used unpowered subs?  What is the advantage of having a discrete subwoofer amp?  Room size is 13'x22'. 
cheeg
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Distributed bass arrays do not result in "fat" bass.
By FAT I mean that unless time correction is implemented the separate sub signals will arrive spread over several milliseconds.

The beater whack on a bass drum will arrive asynchronously to the head resonance, which will arrive multiple times. Depending on the room, subs and positioning, some may arrive before the beater and some after.

IMO, it's as unlistenable as MP3 which are only acceptable in mono.

Perhaps it's because I sat so long in a recording engineer's chair, but there is ONE spot that has the correct image. Period. I never worked in any studio where the monitors, if they were time aligned, were not aligned at the engineers seat. NO STUDIO EVER had distributed bass.
@ieales Thanks for the clarification, but I think I understood you the first time.  As I understand it, "fat" means that the wavefronts from the four subs reach your ears at different times, in the case where they are not equidistant to the listener.  That is not the sound I want.  However, even if you DO correct that (either by spacing the subs the same distance from the listening position or by inserting time delays to get the same effect), the phase will still be an issue, since (as @heaudio123 noted) the phase is a function of the frequency.  Since the wavelength of a bass note varies by a factor of three in the range from 20 to 80Hz, that means (someone please correct me if I'm wrong) that the phase could be perfect for the listener at 20 Hz, 40Hz and 80Hz, but off by as much as 180deg for the frequencies in between.  Having said that, I don't know how AUDIBLE this is, and I'd rather not waste my discretionary spending on something that fixes one of these issues (like time delay) at the expense of the other issue (phase).  And again, thanks for chiming in; I hopefully am learning enough to be dangerous...
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