PVC Pipe Oar Design

Depends...

http://en.wikipedia.org/wiki/Ultimate_tensile_strength#Typical_tensile_strengths lists bamboo as having an Ultimate Tensile Strength of 350-500Mpa and a density of 0.4(g/cc) and carbon fiber at 6370 and 1.8.

The simple way the claim is made is that "bamboo is stronger than CF", which is obvious nonsense. A more plausible claim would be "bamboo has a higher strength-to-weight ratio than CF".

The numbers above give a strength-for-weight ratio of 1250 for bamboo and 3538 for CF. A bit closer.

This is still a somewhat unrealistic comparison, since raw CF is pretty useless. A more useful would be "a bamboo pole has a higher strength-to-weight ratio than a comparable structure made with CF". The wiki numbers for CF laminate are 1600, 1.75, yielding a ratio 914, a bit lower than bamboo.

Every number above depends on several factors, including species, curing, type of fiber and resin, fiber orientation, and construction technique. Without pinning these down more specifically I'd allow at least 50% variability around each of those numbers.

All of the numbers are variable on a number of factors, but it appears to this materials engineer that some bamboo poles will be stronger in certain applications than some carbon fiber composite poles of the same weight. It also seems likely that some CF structures will be stronger than bamboo for given weight.

Given all those variables, each of which has a large range of variability, there are no blanket statements that are true, without so many weasel words as to render them meaningless.

I think it boils down to economics: if you need a shape that is feasible to make from bamboo and you have access to poles that are the right size and suitable species and cured properly, bamboo is a cost-effective material. If one or more of these conditions aren't met, one can design and manufacture a CF composite structure that can meet stringent requirements, but at rather higher cost.