I think all that can really be said is that a googolplex is much, much smaller.
This isn't a direct comparison of a googolplex with Graham's number, but maybe it will help give some perspective:
Some back-of-the-envelope/Mathematica calculations tell me that
$10^{(10^{100})}\approx 3^{(3^{(3^{4.86})})}$
and so a googolplex is between $3\uparrow\uparrow 4=3^{(3^{(3^{3})})}$ and $3\uparrow\uparrow 5=3^{(3^{(3^{27})})}$ (much closer to $3\uparrow\uparrow 4$, obviously).