There are three factors for me in this.
The first is also the most obvious: cost. What are typical rental rates for the area/seaosn/size I am considering, and what does it cost to own it? For most resale timeshares, the ownership cost is pretty easy to figure out, because the acquisition cost is either zero or small enough that you can just fold it into the first year's fees and make the call. For those with non-trivial purchase prices, it gets a little trickier. I amortize it over a 7- to 10-ish year window, assuming zero residual value, at a "reasonable" interest rate of around 5%. You can quibble with the amortization horizon and the interest rate, but it usually doesn't change much.
The second is a qualitative question in favor of ownership: how much time is it to find a good rental, and how much of that will I save by owning? Renting requires searching--and often repeating that effort each year because the place you rented last time is no longer offered/much more expensive/whatever. Owning is usually simpler and that time saved is worth something.
The third is a qualitative question in favor of renting: how likely is it that I will use this ownership as it is every year for the next 10-ish years, minimum. This does not include external exchange. If it is a fixed or floating week, that means staying at that resort every year. If it is a mini-system, that means only using an internal booking. If I'm not sure about future preferences, then owning is a liability because there is friction in using it in any other way. That friction might be in the form of exchange fees and time spent managing the exchange process. It might instead be in finding someone to rent it from me. In the worst case, it might be in the form of an unused week. In contrast, nothing is more flexible than renting with cash, because if you decide you don't want to do that anymore, you can just do something else with the money.
