I think the tree-hugger in me tries to find a rechargeable solution whenever possible. I like devices that I can power with both internal and external options. I usually hook up an external supply, and rely on the internal batteries to act as a safety net in case something happens to the external.
I'll probably run the PSP-2 with the external and internals -- I just gotta remember to remove that sled when not in use!!!
Mine lasts a ridiculously long time on 6 AAs, I'm not sure I'd ever use an external power source unless absolutely necessary. I am using it at 12v (w/ cmr's and a pfa) instead of 48v, but I think I could probably get 14-20 hours from 6 AAs easy.
Aside from the standard battery sled issues (i.e. not forgetting to flip it backwards when not in use), I think it's more reliable powering source than an external battery with a cable that could wiggle or come unplugged. If you flip the sled backwards, I recommend putting some electrical tape on the back side of the sled just to be certain.
That said... damn those pictures are sexy.
Mics: B&K 4011, Schoeps MK5 (Nbobs, Naiant PFA), Busman BSC-1 (K11/K21/K31/K41 caps), Church CA-14 (o, c), Church CAFS, Core Sound Binaurals
Pre: EAA PSP-2, Lunatec V3, Nbox-Platinum, Church CA-9200
ADC: Mytek 192 ADC, Oade Mod SBM-1
Rec: Oade Supermod PMD-661, Tascam DR60D, M-Audio MicroTrack II, Korg MR-1 (32GB SSD mod); Sony PCM-M10, Edirol R09HR; iRiver HP-120
Photo: Canon 5D3, Canon EF-S 17-55mm f2.8, Canon EF 35mm f1.4L Canon EF 24-70 f2.8L MkI, Canon EF 70-200mm f2.8L IS MkI, Canon EF 50 mm f1.4, Canon EF 50 f1.2L, Canon EF 300 f/4L IS, Canon EF 100-400 f4-5.6L IS MkI
Video: Canon HF100