Lammi,
They are not more efficient than a *properly sized* 2 speed pump with a high efficiency motor. The difficulty is in that "properly sized" bit. Few pool builders know how to lay out piping for efficient flow or size pumps accurately. So, they tend to oversize, because they don't get called back if the pump is too big.
The electronically driven motors have infinite speed adjustments so they can be 'adjusted' to your pool on the site. This is better than a too-big single speed, but still not quite as good as a optimized 2 speed. And . . . you pay a price in both dollars and complexity.
If you want a comparison between the Hayward and Pentair pumps, I can't help you with that. I just don't have any service experience with those pumps.
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