On 8x8 the Griffon turned out to be nearly one Pawn weaker than a Queen. Both Queen and Griffon are pieces with sliding moves in 8 directions, making their value scale similarly with board size. (This in contrast to slider-leaper compounts like Chancellor and Archbishop, which will lose value compared to the Queen when board size increases.)

The Queen has a big advantage over the Griffon on sparsely populated boards: it can make distant attacks from 8 directions rather than 4, and can also switch easily between those directions, even between the orthogonal ones. (E.g. an attack on e2 from a2 can on the next move come from e6 through a diagonal move.) This makes perpetual checking, or manoeuvring with checking moves to create attacks on other squares) much easier for the Queen. A check by a Griffon from a2 on a King at e1 can, after Ke2 only be renewed by checking again from the left. There is no way to switch to checking along a file.

Although the Checkmating Applets here cannot do bent sliders (I could not figure out a way for the user to specify those in the move-definition aid), there exists a version that can do this on my own website. (Where the piece is selected by buttons, and you cannot specify your own.) By playing with black there you can see how this 'tunnel drive' indeed often provides the fastest way to checkmate.

[Thought: perhaps we should copy those versions of the EGT builder here too, making the piece(s) selectable through the URL's query string rather than through the buttons, so that we can link the Griffon page to a checkmating applet too. I also have a 3-vs-1 Applet there that can handle hoppers and bent sliders (that cannot checkmate by themselves, such as W-then-B) as one of the pieces. It might be more difficult to utilize that in a sensible way with piece articles, as the mate would require a second piece.]