Taxes should be the same regardless of carrier; they have to do with routing (higher airport/departure/etc. taxes from one jurisdiction to the other.)

As for fees, this is a the big variable. The carrier that issues the ticket (usually the first airline flown) applies a fee schedule that it controls. Depending on that airline's policies, fees may be added which might not be if another airline were the issuer/first carrier. This can result in otherwise very similar tickets having a "bottom line" hundreds or even thousands of dollars different, despite having the same base price. The process is extremely opaque.

Unfortunately, there's no definitive way to know how much the combined fees/surcharges will be on a given ticket, but the sense among many of us is that any RTW ticket issued by BA will carry a higher combined fee total - principally what used to be called "fuel" surcharges (but aren't any more since BA got sued in US federal court over it) compared with comparable tickets issued by other carriers, notably CX and AA. Qantas also seems to be happy to add YQ or similar fees to their tickets, but I can't say (maybe others can) how this compares to BA's fees. The data/anecdote base regarding fees from other Oneworld airline-issued tickets is too thin to say anything remotely definitive.

The best (albeit time-consuming and potentially frustrating) way to see the impact of fees on an itinerary is to load it into the online booking tool and get to the final pricing screen, where you can pull up an itemized list of the taxes and fees. Even then, you won't know what flights/carriers the fees are attached to, but you can at least get a sense of variations by issuing carrier.

For example, I just ran two simple DONE4s ex-Johannesburg, one starting with JNB-HKG (and therefore issued by CX) vs. one starting with JNB-LHR (BA) with JNB-HKG-NRT-LAX-JFK-LHR-JNB as the CX-issued route and JNB-LHR-JFK-LAX-NRT-HKG-JNB as the westbound BA-issued route. The taxes and fees total on the CX route amount to 9,313 ZAR (around US$667) while the BA route total is 15,980 ZAR ($1145.) And that's on only six flights, only one of which (JNB-LHR or v.v.) is actually on BA metal (used AA for both oceanic crossings.) Airport and arrival/departure taxes are the same, so the only variable has to do with carrier-imposed (i.e. fuel) surcharges.