In some ways, it depends on which satellites one is talking about for this comparison to be that meaningful in terms of types of antennae. If i've figured things properly, comparing an RHCP helix against a linearly polarized Quagi is likely to get you a 3dB difference if the satellite is RHCP. Even if the satellite is linearly polarized, on an AZ-EL mount, RHCP may still be the winner, as my experience on an Arrow- equivalent antenna is that linear polarization tends to change from the beginning of a pass through the end (especially on AO-27). I figure about half of time on the average, the linearly polarized antenna is going have mismatched polarization.

A better comparison would be a RHCP Helix against an RHCP Quagi. I have misplaced my copy of the article, but i think the article that inspired the antenna system that i built was based on the QST January 1990 article "Circularly Polarized Quagi Antennas for Space Communications". The drive loop is fed on two adjacent corners to obtain circular polarization. I modeled and then built a phased pair of quagi. The phasing harness had lots of coax in it, but the rest was fairly straightforward.

http://www.qsl.net/kd6pag/nec/q436-5cp1q.html

The modeled gain was 17dBc, and whether i believe that or not, what i do know is that i was able to work AO-40 QRP near apogee.with that antenna, not long before AO-40 went silent.

I had also built a long helix out of copper tubing, but didn't really test it adequately. It was a bit heavy and rather unwieldy by comparison.

-- KD6PAG (Networking Old-Timer, Satellite QRPer)