The overall strength comes from the combination of the two, with increased fracturing/tearing resistance due multiple independent fibers. Tears have a harder time propagating when each fiber needs to be fractured. Materials "fail" by cracks or fractures forming. In homogeneous materials the energy to continue a crack is generally much lower than continuing a tear. Sort of like static vs dynamic friction. Once started a crack will continue with a lot less effort leading to lower material strength. Fibers with a binding agent help prevent this effect.

A fantastic example of this effect is Pykrete which is just sawdust mixed into water before freezing. It becomes stronger than concrete (in tensile strength): https://en.wikipedia.org/wiki/Pykrete

Here's a link to a general material science intro on composites if you're curious: https://in.bgu.ac.il/engn/mater/Documents/LaboratoryBriefing...