Oh dear... okay,
There is no 'fastest' method.
Jessica Fridrich's Website said:
So, what is the best system for speed cubing? I do not think that there is such thing as the best system. One system may better fit one person, other system may be more natural for somebody else. I believe that any system which is worked out into sufficient perfection is good. We should not be comparing systems but cubists. Those certainly are comparable.
(system=method)
- You should choose a method based on what you are looking for in it. Most importantly, you should choose one with an open mind. I'll list the standard 'stages' in solving in the four methods you asked about.
Petrus = 2x2x2 block > 2x2x3 block > EO > finish f2l > LL
Roux = 1x2x3 block > another 1x2x3 block opposite > solve U corners > orient edges, finish L/R sides, permute M layer edges.
ZZ = EOLine > blockbuild f2l (create and place 1x2x2s, and 1x1x2s) > LL
Fridrich = cross > 4 f2l slots > LL
I've not elaborated on 'LL' because thats for you to do. There are several different methods of doing it for all of the one's I've listed (OLL/PLL, COLL/EPLL, OCLL/PLL, Winter Variation/PLL, MGLS/PLL, EJF2L/PLL...), all of which require different amounts of learning and different numbers of 'looks' (algorithms), and can be broken down into smaller and simpler parts (OLL/PLL turns into EOLL, OCLL, CPLL, EPLL).
Each of these methods have various benefits and flaws. For example, after the EOLine stage in the ZZ method, you only have to use R, U and L turns to finish the f2l, and relatively often your last layer is completely R and U turns.
However, EOLine is very difficult.
The fridrich method is good because each stage is 'relatively' simple and there is a lot of room for improvement and development. However, the average solvers move count is not as good as the other methods, and to attain 'full fridrich' requires the learning of many algorithms for the LL.
The petrus method is good because it uses few moves, and after the 2x2x3 block the short EO (edge orientation) stage allows for a quick finish of f2l and OLL, and offers similar chances as ZZ for an <R, U> only last layer.
However using its few moves count to its full potential requires a lot of practice and learning.
The roux method is good because it also uses blockbuilding and has a lot of room for progression in each stage. The lookahead is good too, and it involves few regrips and lots of <R, r, U> turns. However, planning the first stage can be quite difficult and the method isn't always that efficient.
I personally think you should try out every method, see what you like about each one. Fridrich offers the most obvious progression from LBL, but i urge you to look at and play with other methods first. Fridrich is too popular, we need more good people from other methods
useful resources:
http://www.speedsolving.com/wiki/index.php/Main_Page
http://grrroux.free.fr/method/Intro.html
http://www.lar5.com/cube/
http://cube.crider.co.uk/
http://www.cubestation.co.uk/
http://badmephisto.dyndns.org/site/
and last but definitely not least...
www.youtube.com
Use it wisely.