I have installed EMGs in a few guitars that I own, and had similar problems at first. Once I got it working though, they were very low noise, and much louder than any passive pickup I had dealt with. Here is a comparison. DiMarzio's highest output humbucker, the X2N has an output of 510 millivolts. The EMG-81 has an output of 1500 millivolts. This is a big and audible difference. If you are getting similar output to the passive on the instrument, then something is wrong.
In addition, the EMG pickups are solid as a tank, and -very- resistant to feedback and hum. The noise problems that you are having just shouldn't be there.
EMG pickups are wired a bit differently than passive pickups and no attempt is made by EMG to design them to be used in a setup that mixes them with passive pickups in the same instrument, at least as they come out of the box. In particular, they are grounded quite differently. I think that your best bet right no is to remove the passive neck pickup from the guitar, leaving just the EMG. Then go over the wiring with a fine tooth comb, making sure that is exactly as the instructions say. Try that and get back to us.