Are you skeptical that a domain for that scenario exists?
c1 log(n) + c2 > c3
In answer to your rhetorical question: I'd benchmark both. But, I already implemented the simpler algorithm in existing code, and bottlenecks for problems of interest to me are elsewhere.
Also, the more complex algorithm is more likely to have a bug -- which might be elusive, as they sometimes are with complex RNGs. I've found bugs in the published algorithms in DeVroye's book, for instance, and that book is considered authoritative. It's hard to convey just how subversive a parameter-dependent bug in a low-level RNG can be.