Do you want to maximize saving money, or do you want to maximize luxury?
To save money, get the CSR. It has a very low effective annual fee ($150), and the trip delay and trip interruption benefits alone have more than covered the $150 effective annual fee on the CSR card for me. Primary car rental coverage is good, and the Silvercar discount for personal rentals has been great as well. That said Chase does have some nice events and things every now and then.
The Platinum card gives you access to luxury (lounges, reservations, dining, concierge), and can might save you money on luxury travel depending on your travel patterns. But there isn't much in terms of downside protection, other than maybe Global Assist.
Since there are two of you, have you thought about keeping the CSR and your SO getting the Platinum (or vice versa)? They are both good to have and I have both. The effective annual fee is still quite low, and very comparable to the cost of one card + one AU.