WADA doesn't handle testing for any sport - it's all done by the national agencies.
But it gets complicated by the fact that any sport's governing body sets the rules for testing for approval by WADA, which are then administered by the national federations. But WADA has no real power, except to protest to CAS (the Court of Arbitration in Sport) if they don't like how a sport operates (eg [1]).
And yes, some national bodies are more vigorous than others. Famously, Lance Armstrong moved from Nice (in France) to Spain, where the testing was much more predictable and easy to avoid. Also, there were no criminal sanction for the use of performance enhancing drugs in Spain, whereas there were in France.
Thanks, I misunderstood WADA's exact behaviour at international contests.
Complicating the issue still further is that some tests will be carried out by sporting bodies directly, some by national sporting bodies and others by international sporting bodies. And then there are multi-sport bodies like the IOC who will also carry out tests.
In any case, the point is that some countries are more aggressive about testing out-of-competition than others. Depending on the sport, that can make an enormous difference in performance.
And some national agencies are more ... vigorous ... than others.