Native SDI-output vs HDMI-SDI adapter for live stream
For amateur events, SDI may be overkill compared to using simple Component.  The key for long runs is to separate the various components so that they don't degrade.  There is a similar question here about long distance runs. 

As for HDMI to SDI, there should be no quality loss compared to HDMI as both are digital formats supporting full uncompressed HD streams.  The quality of the converter may make a difference, but there is no technical reason that you couldn't have a flawless conversion between formats.  Both support both YCbCr 4:2:2 and 4:4:4, so the color spaces should be compatible either way.