The Rangers hitters had an OPS of .800 during the season and their pitchers allowed a .698 OPS. So that is a .102 differential.
The comparable numbers for the Cardinals are .766-.717-.049.
The following equation gives a good estimate of winning percentage.
Pct = .5 + 1.3*OPSDIFF
That gives the Rangers a winning percentage of .633 and the Cards .564. Using the Log5 method for predicting the probability of winning by Bill James and Dallas Adams (and posted by Tangotiger)
W%(A v. B) = W%(A)*(1 - W%(B))/(W%(A)*(1 - W%(B)) + (1 - W%(A))*W%(B))
we get the Rangers having a 57% chance of winning any given game (this leaves out home field advantage).
The Rangers were even better in September, with a differenital of .298 (.916 - .618). The Cards had .125 (.807 - .682).
The Rangers, however, have a negative differential in the playoffs so far of -.017 (.764 - .781) while the Cards have .096 (.793 - .699). Combining the September differential and the playoff differential in a weighted average by games gives the Rangers a differential of .208 and the Cards .116.