My Chase Amazon physical card is filed away too but I had to dig it out when it had an extra 10% on gas last year!
I got both those cards at different times in my credit journey. I never cracked 5k limit with the Unlimited. My Chase Amazon Prime was close to 10k SL and I moved CL from another Chase card to get it to 10k. I don't know if the Unlimited is a Signature card if you have a higher CL or not, but my Prime card is a Visa Signature and is a Flexible Spending Limit card. It has no FTF. The Prime card seems to me to be a higher-end card but I'm open to others telling me why it isn't. This is not taking UR system into account.
The CFU can be a signature depending on the cli at that time. When I got the CFU, it was approved as Signature due to the sl being over 10K. So yes, it's very possible to get that as a VISA Signature. .
I have both the Amazon and the CFU (and a CSP). Both are great cards. There's no annual fee on either so there's no harm in just keeping them. If it's wallet space you're concerned about, take the Amazon card out and stick it in your sock drawer and just use it on Amazon.
If you don't use Amazon Prime or shop at Whole Foods, it might not be as worthwhile to keep the Amazon card.
CFU and CFF are nice when paired with a CSP or CSR so you can get increased value for the UR points for travel. Amazon is strictly a cash back card. You can get higher rewards elsewhere if you're looking for a non-category based cashback card.
If you're dead set on closing one, pick which one gives you the best value/rewards for your spend and keep that one, and close the other. Or close both and get something else. Up to you.