What is the benefit to using a Blackmagic output vs GPU?

I have an Intensity Pro 4k card that has an HDMI out. I see in FCPX that I have the option to monitor the playback using the hdmi output on the card. Is there any performance benefit to doing this rather than just playing back using a normal GPU output?

Main benefit is proper color accurate monitoring.
Performance gain is 0 (you actually loose a bit of performance when SDI preview is activated).

What is the benefit to using a Blackmagic output vs GPU?

You need a color-managed output that exists independently of the operating system. This way, there's no way for the operating system to change the video levels or colorspace of the signal. With a Blackmagic video adapter card (or box), then the only thing that controls the video is the Blackmagic software (Desktop Video and the application).

Read pp. 660-661 of the Resolve 14 manual: "Limitations When Grading With the Viewer on a Computer Display." This goes into some detail why you cannot accurately monitor directly from the computer and operating system (and/or the GPU). You have to have a color-managed output, like one from a Blackmagic display card, preferably on a calibrated Rec709 display.