I don't have either of these, but I can regurgitate some common knowledge that I've picked up and witnessed.
The Grasshopper can do laser vomit well from Mediums out to Large Lasers, and can mount it's weapons higher than the Black Knight can. It's not much of a front-liner, but it also won't crumble under fire.
The Black Knight is restricted to shorter range due to having very low hardpoints, but has very tanky hitboxes. I've heard people say that it's decent with an XL, because of how long you can keep those side torsos alive. Head hardpoint is nice and high, but in practice it really only adds the the zombie capability of this mech.
If you want to brawl, get the Black Knight. If you want to snipe or skirmish, get the Grasshopper instead.
EDIT: Some people say that the Black Knight isn't very good at brawling. On release it wasn't, but then the quirkening 2.0 happened only weeks later and the chassis got a sizable buff.
Edited by Hornsby, 19 January 2016 - 10:13 PM.