Hi yulnidaq,
Looking at the specifications for the device, the counter input will have ~50kOhm bias resistor at the end of the line. This is what your signal would see as the input impedance. Also, see the note about the tolerance of the resistor near the bottom of page 2.
NI 6013/6014 Family Specifications
http://www.ni.com/pdf/manuals/370844b.pdf
I would recommend taking a look at your signal with a scope where it connects to the 6014. See what the voltage levels actually look like and if the signal looks noisy. Do you have a test signal other than the PMT that you can use for debugging? This will be helpful to ensure that both devices are reading the correct values. Use on of your digital lines on the 6014 to generate the pulse and ensure that you get a count on both devices for each.
Also, are you doing a simple edge counting measurement or another type of measurement?
Regards,
John Bongaarts