Quarries take between 2 and 9 MJ per tick, depending on how full their internal energy storage is. it takes 30 MJ for them to break a block and I believe 10 MJ to move.
The engine MJ/t amounts are as follows
Redstone - 0.05 and can no longer be hooked up to a wooden pipe. In order to draw any power out of a redstone engine into your system you need to attach it directly to an energy storage cell. This is a waste.
Sterling - 1 MJ/t. A stack of coal will last you around half an hour
Combustion - I believe the amounts are 1 MJ/t off lava, 3 off oil and 6 off fuel. used to be 1/2/5 but was rebalanced with the other engines from forestry and TE
Steam - 2 MJ/t. needs constant supply of water will shut down before exploding
Magmatic - 4 MJ/t needs constant supply of lava will shut down before exploding
Peatfired - 1 MJ/t lasts several hours off 1 stack of peat
Electric - between 1 and 6 MJ/t depending on what electron tubs you have in it. default is 2 MJ/t off 6 EU/t
Biogas - between 1 and 5 MJ/t depending on what fuel you have in there. can last quite a while.
Hobbyist steam - almost identical to the TE steam engine and 2MJ/t, but you can also pipe steam in from a boiler if you want. If you run out of water in the engine, pumping water into a hot and dry steam engine will make it explode.
Commercial steam engine - 4MJ/t runs off external steam. needs 2 cobblestone waterproof pipes or 1/2 golden water proof pipe to fill up with steam.
Industrial steam engine - 8MJ/t runs off external steam. needs 1 golden waterproof pipe to fill with steam.
finally - not really an engine, but useful in this situation: the energy storage cell. variable charging inputs and outputs from 0 to 125 MJ/t. Holds 500,000 MJ. a 9x9 quarry next to one of these set to 6 MJ/t output will dig from around layer 70 to bedrock without needing to recharge.
hope this helps ye at all. My favorite technique is just to have 9x9 quarries running off of energy cells, which I charge off 3 other energy cells which are plugged into my bases boiler. This way I can charge with a max output of 3 cells at 125 MJ/t even though my base only produces 114 MJ/t