I have both in my tanks. They make different sounds, but neither is silent.
Positives for Vortechs:
Broad flow, which I see as a positive.
Less visual obstruction in the tank, also positive.
Historically good warranty support after the official warranty has run out.
Good durability history.
Negatives for Vortechs:
Price.
Wet side failure if you buy a pre-QD used unit.
Cannot angle (although broader flow covers for some of this).
Can only be mounted on an area where the exterior is accessible. This can be a problem if your tank is less than 2.5" from wall or you want to mount to an overflow box.
Will not integrate to Apex for feed mode other than off (cut outlet) or with WXM. Personally I don't change mine during feeding, or I turn it off.
Neutral for Vortechs:
Nicer programming interface (but only if you have a Reeflink and learn the quirks of Ecosmart live). WXM if not, although I haven't used those.
Positives for WAV pumps:
Price.
Excellent warranty support within the warranty period.
Much easier to direct flow, mounting more robust.
Integration to Apex without a WXM if you're an Apex user.
More possible mounting locations than Vortechs, especially with tanks that do not have 2.5" to the nearest wall.
Negatives for WAV:
I don't like the Neptune interface as much.
The narrow flow pattern. I've been thinking about making and printing a different front housing to try to make it more like the Vortech pattern.
I really don't like the cords in the tank. I don't care how large they are outside the tank, but I don't like them inside.
Good luck with warranty if you lose your receipt. Sort of suspect it's iffy after the warranty expires too (well, it is expired, but we're comparing to Ecotech who often does support post-warranty).
Neutral for WAV:
Extra 1-link needed after the first three units, although not an issue if you have another EB832.
Not nearly as much durability history, although other than wireless network issues Neptune products are generally pretty robust.