Both brakes don't work well
Even if they were heavily contaminated, pads should have enough grip to lock up against hand pressure. 

My first guess is that your pads are worn to nothing and you're trying to grip the rotor with the pad holders. New pads would be the first order of the day. 

The second thing would be that you've tightened up the slack adjustment too much or that you've clamped the brake line at the brake so high that you have no brake travel left. So you're essentially hitting the limit of the brake when you squeeze, rather than grabbing down with your caliper. 

I'd take it to your local bike shop. A one minute look over would tell them if you needed new shoes or brake cable adjustment. 



Since replacing your pads resolved it, it looks like either pad contamination (or brake setup) was the problem. To make sure your rotors don't recontaminate your new pads, I'd clean your rotors with some isopropyl alcohol (rubbing alcohol) from your local pharmacy / drug store and make sure not to get anything oily (such as fingerprints) on the rotors.