It's 3 dB for sailbaots vs 6 dB for powerboats, not 3 ft vs 6 ft.Someone correct me if I am wrong, but, I believe you would not want to use the 6' antenna. Those are intended for powerboats that will be on the level. The 3' antennae have wider lobes of signal radiation than the 6'. When you are heeled over, the 6' antenna will have maximal power directed toward the water and the sky.
Marine VHF frequencies are 156-162 Mhz, which is a wavelength right around 6 ft. The 6 ft antennas are full-wave, the 3 ft antennas are half-wave. For esoteric engineering reasons, you should avoid the full-wave antennas unless you know what you're doing. Stick with half-wave. (Most "6 ft" antennas are just a 3 ft half-wave antenna on top of a 3 ft fiberglass pole, so don't assume you're getting more for your money by buying the taller antenna. Likewise, the 8 ft antennas are a 3 ft antenna on top of a 5 ft fiberglass pole. The height affects how far your antenna can see over the horizon, which is why sailboats try to mount it on top of the mast. The Coast Guard puts tall antenna towers on top of big hills near the coast to maximize range.)
3 dB vs 6 dB (vs 9 dB) determines the beam pattern. Imagine dropping a donut so the antenna goes through the donut hole. The lobes of the donut roughly correlate to signal strength - it's stronger out to the sides, weaker up/down.
A 3 dB antenna has fairly round lobes. It's signal strength is weaker overall (only 3 dB), but more evenly distributed across a wider range of angles. A 6 dB antenna has stronger signal, but it's like a squashed donut - the lobes are stretched out closest to the horizontal. So if you tilt the antenna a bit, you quickly get into the smaller parts of the lobes and your signal strength is actually weaker than for a 3 dB antenna. West Marine actually has one of the best pictures demonstrating this that I've seen.
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Anyway, since a sailboat is frequently heeling, your antenna is unlikely to be perfectly vertical. So if you get a 6 dB antenna and are heeled, you're likely trying to transmit and receive at an angle where a 3 dB antenna would actually perform better. That's why they recommend 3 dB antennas for sailboats, 6 dB antennas for powerboats (which tend to stay level more than sailboats).
And yeah, the antenna affects both transmit and receive signal strength. There's a common misconception that your antenna only matters for transmit. The math for receiving and transmitting is symmetrical. So whatever dB gain the antenna gives you for transmit, it also gives you for receive. (Think of it as talking through a cone megaphone so you can be heard further. But you can also put the cone up to your ear to hear further.)