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You won't get different performance between screen sharing and Apple Remote Desktop. Scaling and performance of screen sharing will be limited by the speed of the network, as well as the speed of the two hosts. I'd be very surprised if any of these controllers were remotely capable of sustaining 4K output, too. Graphics that far back was usually NVIDIA GeForce 7300 GT, GeForce 8800 GT, Quadro FX 4500, or ATI Radeon X1900 XT. You're going to be limited by the resolution of the Mac Pro graphics controller, which is old and slow. For comparison, we're coming up on the release of Mojave macOS 10.14. That Mac tops out at OS X 10.7.5, which is a very old release. That A1186 model number is associated with a MacPro1,1 Mac Pro 2006.
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