The Volkswagen Transporter has a towing capacity of 750kg for an unbraked trailer and a maximum towing capacity of 2800kg for a braked trailer. That's 6000 pounds.
Good question. I don't usually think of towing stuff because that's seldom been a part of my life.
3500 pounds is what Honda lists for towing capacity (same as a 2WD Honda Pilot, even though an AWD Honda Pilot with exactly the same engine and transmission is more like 5000).
If towing capacity is defined as "what people can expect a thing to reliably do for many thousands of miles, in a row, over and over again" then I think a bone-stock Odyssey would roll over and die with 6000 pounds behind it.
Slow trip to the dump that's right over there across flat terrain? Sure, probably OK if it's rather heavy. Through the Appalachians? No; that's sounding like a bad day.
And the usual variables can be wiggled: A better transmission cooler can be added without too much difficulty (and Honda used to sell kits for this, themselves). There's seemingly-reputable companies that sell air suspension (read: adjustable) helper-springs for many years of Odyssey, and reports are that they're not particularly hard to install (as a DIY, in the driveway). Weight-distributing hitches help a ton (literally), but IIRC Honda doesn't list a separate capacity for that.
There's other vans with similar interior volume and features that are stated on the door sill sticker to tow trailers better.
And there's certainly some things that trucks like an F150 can get very right. Towing is one of them.
If a person wants to occasionally haul a decent-sized camper around or something, then owning a pickup truck may be exactly the right solution.
Transmission coolers and suspension kits are great but one of the things that’s really even more important is the ability to stop it comfortably. I think it’s prudent to build in a safety margin of at least 25%. More is better here.
And ideally, the trailer should have its own brakes and (mostly!) stop itself.
I've never found the brakes on an Odyssey to be particularly lacking on their own, even when loaded heavy in mountains. They're fine. 2-pistol calipers, decent-sized rotors. Nothing fancy, but also nothing lacking. The ABS behaves sanely.
The only thing I see people complain about is warping, but the causes of that are very varied (and may have nothing to do with anything actually being warped).
Like many vehicles, they get a lot better with good rotors that have cooling improvements, and well-selected not-ceramic pads.
It goes from "yeah, those are fine" to "Holy Toledo. My sunglasses just flew off of my face, and I think the seatbelt hurt my shoulder (but there was no crash, so it's fine)"
