Personally, I'd vote for Hyatt as hotel card for the long run. My biggest regret in the 10 years I've been at this hobby is not jumping on the Hyatt bandwagon sooner. I get it now. With that said, why go with the "or" option when the "and" option is open.
The "cost" of points it takes for a redemption can be as low as 3,500 points for an off peak cat 1 property and as high as 45,000ish points for a peak cat 8 property. There is a a peak and off peak chart to provide an idea of how many points you will need at a given property. The personal card gives you a free night certificate at a cat 1-4 property each year. The Chase UR ecosphere makes it easier to earn points faster with various cards that can be transferred to Hyatt 1:1. This is quite valuable. I did a search for a stay at WDW area and the Grand Cypress is $1,120 for 4 nights July 1-5. That would be about 89,600 CSP points through the portal. The same 4 night in the same room would cost 60,000 UR points by transferring them to Hyatt and booking with hotel points instead. Additionally, they can be transferred 1:1 for IHG, Marriott, and various airlines. Freedom 5x, CFU at 1.5, Ink Cash 5x at office supply stores, cable, internet and phone, Freedom Flex is 3x for dining and drugstores. With a transfer to your CSP account these points retain a .0125 cent value through the portal giving you flexibility if you need to purchase travel through the UR portal.
Meanwhile, I rarely see a Hilton property for less than 50k and often 120k for standard room. Hilton no longer has an award chart and the pricing is dynamic, so one night could be 40k points and the following night could be 80k. The individual Hilton cards do earn more points for certain purchases like groceries and gas but they are only good for Hilton stays. So that to me, reduces the value of the points earned for spending on the card. You do not get a free night certificate unless you hold the Aspire which is $450 a year. We have 4 Aspires in this household and I get excellent value from them. I put no spend on them unless I am at a Hilton property. You can also purchase Hilton points for about 1/2 a cent per point and I do that as well. But I only use Hilton points for outsized value redemptions. The same dates of 7/1-7/5 at the Hilton Bonnett Creek are $1334.25 and with points are 240,000 points. Id have to spend $80k on non category spending to earn 240k points for this stay on the Hilton Surpass or Hilton no fee card. I'd need to open 2 Hilton cards, both with a fee to get enough points for this stay.
But I'd only have to spend $40k with a CFU to earn the 60k points on the same non category purchases that I could transfer to Hyatt for the stay. Meanwhile, I could open one Ink Cash with no fee and earn more than enough points for the Hyatt stay since you can transfer those points to your CSP.
Anyhow, I'd say go for both but start with Chase while you are under 5/24 for the long haul. Additionally, I'd suggest looking at the options for the properties you may be thinking of staying at and seeing what the point cost will be for a similar stay and go from there. Hope this helps.