Years of lifting have made me rather big too (186cm 102kg), but that does not automatically mean stiff.
Out of curiosity I tried a couple of Yoga exercises and found out that I'm flexible enough to do almost all of them but the most exotic ones. Makes sense, most lifts require a lot of flexibility since their range of motion is very big.
Yoga does have its place, though I'm a die hard advocate of good old iron pumping, especially the 4 power lifts to strengthen the entire body. Overhead press, deadlift, squat and bench press. There are no other methods that strengthen your body as much as doing those basic lifts with heavy weights. The problem with yoga is its limited to your own body weight, eventually you reach a level you can handle up to 2-2.5 times your own body weight in several exercises. Especially the the king of exercises, the deadlift. The majority of untrained people can deadlift their own weight right from the start, the pros can do 3 times their own weight.