Long-time DVC owner (since 2006) more recent Hyatt owner (since 2015) so I'll add some color from our experience with the OP that hasn't been mentioned yet. One HUGE distinction between the programs in my experience is the availability of discounted cash-reservations via Hyatt Residence Club. DVC has nothing like that.
I should say that we only use Hyatt Wild Oak Ranch, so my experience with "trading" is limited to that resort.
I picked up a 1400 point week at Wild Oak Ranch for $1. We've had no problem using that to get split weeks at WOR when we want them. And, once you're a member, HRC offers some very attractive cash rates to members for additional days. I've found that I can pick up two additional three-day weekends on a cash basis, for the same cost of annual dues of an additional week. No acquisition cost, no ongoing commitment. And much, much greater booking flexibility. For example, two weeks ago I booked Easter weekend and Memorial Day weekend at WOR on cash via HRC. Arriving and departing the nights, I want. So really great flexibility for us. (The posted rate at Hyatt.com for the room was $587; HRC rate was $260.)
As for comments about how it's impossible to justify the cost of DVC. I might agree, if you don't plan to ever sell. For me, I just divested of a portion of my points that I acquired in 2007. My kids are getting older and we have routinely found ourselves with banked points each of the last two years, so it was time to downsize a bit.
After accounting for all costs -- acquisition, sales commission and dues paid in the last ten years -- each point I used during the period I during which I held the contact cost me .32 cents. Points rent for $13 - 15 range. At .32 cents, I was getting a 2-bedroom unit at the most popular resort on earth for less than $25 a night. Countless great memories at almost no cost. If you get in and out via resale, you're downside risk is pretty minimal. Or, in our experience, non-existent.