Compete with sunlight? Sure, easily, especially in shade. My 600EX-RT through a small soft box is still sufficient to compete with sunlight and give primary lighting from the flash if I want it to. The key is to a) be close enough and b) shoot fast enough.

A flash is not sustained light, it is very intense light for a very short time. The longer your exposure, the more time ambient light has to accumulate on the sensor. Shorter exposures give your flash a higher degree of influence. When you hit the HSS point for your camera, you will lose a fair bit of power, but it may still work out to be worth it for the extra shutter speed you can get to reduce the ambient further as well.

Adding additional flashes to the setup makes it even easier to accomplish, allowing shooting from further away or will slower shutter speeds (though still pretty fast).

I'm not sure what you mean by blowing the background. That normally means it would be all white, which doesn't makes any sense in this case. To blow the background to white, you simply would over-expose the background and wouldn't want flash. If you meant you want the background to be black, that also doesn't make any sense as you would have to be many (6+ at least) stops brighter than the ambient light for the time exposed, which is an insane amount of light, far, far beyond trying to simply compete with sunlight.

From your update, being 15 feet away is certainly a big part of the problem. That's forever away during outdoor shots. You basically want the flash as close as you can get without being a) in frame or b) casting undesirably hard shadows. Light power falls off exponentially over distance, so the closer you can get, the more power you have.

Also note that if you can't completely blow the background without the flash, you really aren't going to be able to do it with the flash because the flash is adding light to the foreground which means that exposure of the background will go down, making it less blown.