I would go with the AJ-PX270.
Videomaker – Learn video production and editing, camera reviews › Forums › Cameras and Camcorders › Professional Camcorders › Panasonic AJ-PX270 or Sony PXW-X180? › I would go with the AJ-PX270.

I would go with the AJ-PX270. B&H has a great $500 off promotion that shows up after you add to cart ($5249). This early bird deal may be due to fact Panasonic made an odd choice to go with the older battery type and the px270 currently lacks full 24/30p support for the LongGOP compression settings. The only other complaint I have is the power draw is insane. The D54 batteries last approx 60-80mins.
I picked up the camera thinking I could fly under the radar until Panasonic released the update, however, I ended up getting multiple requests for 24p for long 15+hour shoots where its not practical to shoot in Intra100.
The PX270 plus two 64gb P2 cards and 4 used CGA-D54 batteries should be a nice fit for your budget.