Depends on what you want to accomplish. I've owned both; I had the 853s for a short time but didn't know about the 3-wire battery packs at the time, so any loud venue resulted in distorted recordings. The CSBs were good because they were able to handle higher SPLs without distortion and were smaller and easier to conceal. They didn't sound as good as the 853s, though (I had card caps in there) and Len at Core Sound is not a personable guy. There are some other choices out there now like Giant Squid and Church Audio, you might want to do a search about those mics on here. They seem to be more reasonably priced than the Core Sound stuff and I haven't heard anything bad about customer service from either company.
Are you talking about the regular 853As? They have 1/8 connection like the CSBs and run on standard 9V battery power. The 853RXs are phantom powered. Never heard of anyone running the RXs with a 3-wire battery pack. You need a separate phantom box like the Denecke PS2 or a preamp w/ phantom power like the Sound Devices MP2 or Mixpre, to power the RXs.
Any hoot, definitely get the 853RXs. Phantom power is king. Better SPL handling, better dynamic range. I recorded the Black Crowes last year in a tiny venue. The 853RXs took a full shot from the head-level PA system and had no distortion or issues in my recording (I can't say the same for my ears
). And everyone knows how loud the Crowes can be. No brainer, 853RX over the CSBs all day long.
As far as 853As vs CSB, I have not compared them. But I'd have to give the 853As the edge because of multiple caps. .
Hope that helps. Good luck!