I had exactly the same sensation when I changed the 707 in my hellraiser with the 81-7. It seemed that the 81-7 had very low output. I liked the tone, but there was huge lack of output and gain.
But the output should be exactly the same on both pickups,
http://www.emginc.com/content/wiringdiagrams/EMG-81-7_r0230-0064A.pdf
http://www.emginc.com/content/wiringdiagrams/EMG-707.pdf
http://www.emginc.com/products/index/89/36/1
These both seem to say that they are almost identical