I really think either could work. For the most part, the only rougher terrain is between Marmora and Bancroft. Most of the other trails and gravel roads are well suited to a gravel bike. What kind of tires do you have on your gravel bike?
On second thought, you might overall find the route more enjoyable on a hard tail for some extra comfort. My route includes some gravel road options to break up the trail, but many riders just stay on the rail trail the whole time between Haliburton and Bancroft. Personally, I find that a bit tedious.
That looks like a nice new ride. As a rough estimate I think that wheel/tire set-up will be perfectly fine for 75 - 80% of the COLT. The rest you may feel a bit underbiked, particularly the section that is prone to being sandy by Bancroft. I know from Haliburton to Campbellford is pretty smooth sailing on rail trail and gravel roads. So I'd say it's not a bad choice for the COLT. Perhaps your biggest threat are the bugs
As for the BT 700 people have certainly completed the loop on 700 x 37/38 but personally I prefer a bit more comfort on this route. I'm going to try it this season on 650B wheels with 2.1 tires. Slower on the smoother stuff but will be more capable on the rougher unmaintained roads and trails.