They're pretty much orthogonal.
PEG is a particular parsing technique. Combinators are a technique for implementing parsers.
You can write a parser combinator library which uses PEG or packrat algorithms underneath.
In this blog post, the library that I'm using is basically building LL parse generators, not PEG. But you could easily implement a PEG-based combinator system.
I didn't do that, because I didn't want to get bogged down with explaining too much about parsing algorithms. The LL/recursive descent approach is pretty easy to understand when you see the grammar code. For PEG, I would have needed to spend more time explaining the algorithms, and the post was already too long!
The Python syntax is a bit klunky. The Haskell equivalent is on par with the PEG. I don't know how they compare as the grammars become non-trivial.
Do you know of any benchmarks of different parsers, especially combinator libraries?
The article claims recursive descent is tedious and error prone, but I've not found that to be the case. In fact, combinators like match, many, and opt map easily to either if/while or higher order functions.
I also think people tend to focus too much on LL vs LR vs whatever. Clang parses the entire family of C languages with a hand-written recursive descent parser + pratt parsing and it's well-known for its error messages, speed, and memory usage. I would also say it's very readable and pleasant to work with (for a C++ parser of course ;)
And if you think these things are toys, consider e.g. http://hackage.haskell.org/package/FpMLv53 is used to process transactions worth billions.
