Stroker advantage

Everytime I talk to a fellow car guy weither it be a ford Chevy or mopar guy they always talk about their "Stroker motor" I even see it in here alot you see a ton of 408s and other stroker variations. Ever time I talk about my engine build the first thing people say is why ain't you gonna stroke it? So this leaves me to question... what are the power advantages to a Stroker? Other than cubes? For instance take two identical combinations same intake carb, heads, cam, compression, exhaust, bore, pistons everything exactly the same one has a 3.58 the other has a 4" stroke how much more power are we talking? 20hp 50hp.....? I'm just curious and inquiring minds have to know.