Carbon fiber (and all woven composite reinforcements) are strongest in the direction of the weave. If you laid all your fabric in the same direction then most of it's strength would be in that direction but.... nobody who knows what they are doing would lay all their fabric in one direction if they expected multi-directional strength.
When I make cf plates, I take a number of steps to increase the multi-directional strength. First, I switch the direction of the weave for each layer. Second, I add some layers of biaxial and triaxial carbon fiber. Third, I thicken the plates with layers of recycled no-woven carbon fiber mat which, instead of a one-directional weave pattern, it has the fiber laid out in a random matrix which adds rigidity in every direction (as well as reducing cost as this material is very thick on it's own). Fourth, I add carbon nanotubes to the resin which increases rigidity by approx 30% (depending who you ask and if you are buying or selling).
The choice of weave also also makes a huge difference. When I want the most rigid parts possible, my preferred fabric for the outer cosmetic layers is a 4x4 twill which comes out noticeably more rigid than the more common 2x2 twill and plain weaves.
There is also the type of resin to consider. I don't just mean epoxy or polyester resin. There can be huge differences in the physical properties just between epoxy resins. And... don't get me started on the curing schedules
All this makes accurate strength comparisons extremely difficult. Carbon fiber, as a general point is stronger than steel by both weight and volume. But... for reasons described above, you can't say by how much unless you have the two parts side by side to compare.
You also have the added complexity of people using alloys rather rather than pure metals these days. I read about a recently created aluminum alloy that is stronger than steel and titanium. I've had bars of T6 that felt stronger than some low quality stainless steel products I've seen. Plus, the strength of steel is also somewhat dependent on how it's made and prepared too. There is a world of difference between, for example, the differentialy tempered, folded and laminated steel on my old martial arts practice sword and the cheap nasty Chinese stainless steel on the kitchen knives I got as a wedding gift from my distant relatives...
Anyway, net net, if made properly, my cf parts will be stronger and lighter than equivalent steel ones. That's the part I know. The part I am assuming (based on what I've been told) is that a lighter gantry will increase speed.
Also, carbon fiber is less sensative to heat distortion than steel so it should be a generally more stable material for this purpose. It doesn't rust either, which is a plus because I want to put this machine in my garage.