I don't think a Pi is a good replacement - it does not have the power to do general purpose transcoding, and RAID would be a problem (maybe you could do something with a USB hub - it apparently has USB3 which may make it viable). Have a read of How does a Raspberry Pi 4 truly compare against a modern desktop CPU? about the relative performance of a Pi - in summary a Pi is about 1/6th the power of your processor for general tasks, but I'd imagine its a lot worse for encoding tasks, depending on the codec.
A NUC would absolutely be a far better replacement, and will be a lot more power efficient then your current rig (of-course it will cost a lot more then a Pi). It would also allow you to do RAID if you can work out how to attach 2 disks to it. (Likely you would need to use SSD which would be very expensive compared to spinning disks, although theoretically you could use an external USB disk). I expect a modern NUC would use a lot more electricity then a Pi, but a lot less then your 6-7 year old i5 - especially if you tune it as you might a laptop to reduce its power consumption at idle.
Have you considered NOT using RAID and instead doing some kind of software mirroring, archiving to an external disk - for example using rsnapshot or rsync periodically (which could mean loosing the latest changes, but if its just a media center, so what. If you use rnapshot instead of rsync you get cheap point in time recovery. )
