One way is not the "easy way" Both require hard and dedicated work.
Dude, I already posted my advice on this situation in an earlier post..... I said if you are over 12% BF, get to ~12% first then get your strength up. If you're over 2xBW squat, then try to get even leaner.... If you're a single leg jumper, get to ~10% ASAP and then build up your strength. This is all just my opinion.
In your terms, the "hard way" of losing fat and building muscle is only going to be possible if your within certain body fat and strength levels as I already have stated... If you're 7% BF, you're not going to get leaner while getting stronger. If you're 20%BF it's pretty easy to build muscle and lose fat simultaneously. But if this 20%BF guy has a 3xBW squat and 2xBW Bench, he probably won't gain much muscle/strength, if at all, if he's trying to lose fat.