The 70-200 f/4 IS has pretty much the same image quality. It has the biggest aperture at 200mm (f/4 vs f/5), but lacks the extra 100mm on top of that. The 70-200 f/4 IS focuses internally (meaning it's bigger, but also sexier). It's also less heavy (70-200 IS is 760g, the 70-300 is 1050g).
Personally I also considered both lenses. The 70-200 f/4 IS was also cheaper than the 70-300 where I live; 200-250eu cheaper to be precise). I decided to go for the 70-200 f/4 IS, because I don't need the extra 100mm so much. I required IS, I like somewhat shallow DOF, but I'm on a budget and I didn't want a heavy lens. I'd use it mostly for (candid) portraits, nothing requiring over 200mm (I'm on a crop body).
I can see many people would go for the 70-300. It's just that bit more versatile. Anyways, IQ should not be a differentiator between the two; but like I said, there can be others (namely weight, price, and largest-aperture difference or constant aperture benefit).