2010-2011 stats (I am ignoring last year's playoffs, simply because the sample size is too small for Paul to actually make any good judgments ... yeah yeah, his performance against the Lakers was great, but it is not indicative of his average quality of play. Remember how many 3s Lebron his in the Celtics series? And then he started hitting less? Regression to the mean, baby); also, just looking at last year, and not career, if someone else wants to do the career comparison feel free.
Shooting (not using TS% ... Rondo is an awful free-throw shooter, which we all know, and that skews his TS% down a good degree. Yes, it is important he can't shoot them and he needs to learn, but for looking at actual production on the offensive end of the court I am looking at normal FG%)-
Chris Paul 15.8ppg at 46.3%
Rondo 10.6ppg at 47.5%
Advantage here is Paul, but honestly not by that much
Play-making-
Chris Paul 9.8 assists per game (Assist Ratio 38.0)
Rajon Rondo 11.2 assists per game (Assist Ratio 44.1)
Advantage here is Rondo by a good margin
Rebounding-
Chris Paul 4.1 rebounds per game (w/ rate 6.9)
Rajon Rondo 4.4 rebounds per game (w/ rate 6.2)
Advantage here Rondo, but not by much
Steals-
Chris Paul 2.4 steals per game
Rajon Rondo 2.2 steals per game
Advantage Chris Paul, but by a very small margin
Defense-
Unfortunately not a lot of stats to work on here. But in 2011 Chris Paul was on the All-NBA Defensive Second Team, and Rondo was on the All-NBA Defensive First Team. From a subjective standpoint, watching games, Rondo appears to be a better defender, and is recognized around the league as such, so advantage Rondo.
Turnover rate-
Chris Paul 8.6
Rondo 13.6
Advantage Chris Paul, by a big margin
Usage rate-
Chris Paul 22.2
Rondo 19.7
(no "advantage" here, because usage rate isn't really a stat you can say someone is better or worse at, but it is good to look at in the context of other stats)
I am not looking at PER or WP48, because those stats are known to be fairly unrepresentative of actual play (especially PER). WP48 is very contextual, in that the team around you has a very large effect, and we are trying to ignore that for right now.
So what are the differences here? With Chris Paul you have a better scorer, but not by much (and it is worth noting that this marginally higher scoring is due to a higher usage rate, due to not having as many scoring options around him). With Rondo, you get a better defensive PG and better play-maker (though, too, Chris Paul's higher usage rate will necessarily decrease his assist ratio ... however, even adjusted for usage Rondo is better here). Paul has the advantage of being a better ball-handler and won't turn it over as much (though it. In other categories they pretty much break even.
Honestly, I don't think the differences are as big as some people are making them out to be. Both are very good, elite players, with their own unique set of skills. Saying one is "clearly" better than the other is both inaccurate and disingenuous. Instead, you should be focusing on which one fills a need.
Chris Paul adds scoring, and manages turnovers better. However, the scoring advantage is relatively small, and would likely decrease (even as his assist ratio increases with the Big 3 around him). So his main advantage is that the offense will run more smoothly. However, he isn't as good defensively (though that could easily change in the Celtics system, and he isn't a complete schlub defensively). On that level, it does seem that Chris Paul is a better fit, though it is by a pretty small margin, and as the Perkins trade showed, team chemistry goes FAR beyond mere stats.
(So, basically, I am telling people to stop exaggerating Paul's strengths and Rondo's weaknesses and look at this more rationally ... I mean, hell, the same people calling for Rondo's head were the ones who were most p---ed off by the loss of Perkins. Different situations, yes, but team chemistry is something you can't quantify statistically but has a MAJOR effect).