Are BuildCraft and IndustrialCraft compatible with each other?

Currently no. However if I get off my lazy butt I am halfway through writing a mod to make a new BC engine that runs off of IC power. Keep a eye out for leftler on the Minecraft forms. (I will post a link here too when it is done.)

It appears I was too lazy and someone beat me to it. Here is a link to a mod that will do it.

Mod that allows you to get MJs from EUs is Forestry, you can use Electrical Engine to do that.

Electrical Engines require 6 EU/t to produce 2 MJ/t. They accept packets of any size (so can be connected to HV or extreme voltage cables directly). Will not ovearheat. Can be upgraded to change either power requirements or amount of produced energy with electron tubes, details on project's website.

Sadly it does not add a generator able to run on MJs to produce EUs.