Depends very much on where you want to go and how you want to get there. If it's an international flight and/or in a premium cabin, an airline/SPG card will usually be better.

However, if your family vacation is simply a domestic flight in coach, cash back will probably be better.

To transfer SPG to an airline for that domestic ticket, you'd need $20,000 in spending and be subject to capacity controls.

On the Arrival card, that same $20k spending would earn you around $440 toward the retail price of the ticket. That would cover most domestic fares easily. (The ticket would also earn frequent flyer miles itself, probably in the neighborhood of $50 value.)

The best research you can do is to try to understand how much tickets "cost" in each scheme. Look up the award charts for the airlines you could fly on your routes. Plug in typical dates into their award searches to see availability. Compare to cash prices.