This is a question that is really of interest to me at this time because I have been playing with both. I haven't been doing so in the respect that I try one and then the other, but rather, I have been trying the "natural swing" as taught by Brian Sparks and others where you let the front foot/heel do what it naturally does without worrying about it.
I must admit that I have kept my left heel down for so long that it really feels most comfortable for me to do it. Letting it raise makes my swing feel a bit "sloppy." Nonetheless, doing so didn't affect my shot-making, but it really affected my enjoyment of the game. Letting the heel raise, along with other "non-conventional" movements, such as allowing the head to move freely and the weight to transfer almost completely onto a straight back leg, really takes a lot of strain off the body. To give you a sense of this, do a very slow motion swing, and any time you find your body feeling pain/strain somewhere, allow the body to move into a position that alleviates the strain. Raising the front foot reduces the strain on the lower back and knees.
I don't know how old you are, so YMMV. In fact, If you're young, none of this will make sense to you...YET. But at 56, I am finding that I am really tired and sore at the end of my rounds. I am nearing done after 14 holes and there are plenty of times that I can hardly swing on holes 17 and 18. With this "new," more fluid swing, I'm coming off the course with almost no pain and even feel like I could play more.
(On a related note, I'm reading George Knudson's book Natural Golf Swing, and I'm really liking it.)