The main differences are :
As you stated, Hidalgo's teams played very well. The "carré magique" was typical fluid, pleasant football in a very "French" style. Domenech's "2 milieux défensifs" has been laborious since the first game, and is a complete anti-thesis of both good offensive football and good defensive football.
Hidalgo qualified France against harder opposition. Sorry if this might sound condescending, but Hidalgo didn't play Ecuador, China and Costa Rica and other third-rate international opponents half as frequently as Domenech does. Qualifying for international tournaments has become a relatively easier deal as well, a point I'll expand on. But when comparing records, it's worth keeping in mind that Domenech has padded his out with loads of crap matches that would have been a joke to lose.
Qualification for their World Cups. Seriously, Domenech's qualifications make Hidalgo look brilliant. 2006 World Cup? Domenech took 10 points from the first 6 matches of qualification (in a group with Israel, Faroe Islands, Eire, Switzerland and Cyprus), 6 of which were against the Faroe Islands or Cyprus. Although Zidane, Thuram and Makélélé had retired, they returned (apparently thanks to certain sponsors shared by Zidane and the French NT), and -only just- managed to qualify France on the last day thanks to a draw between Switzerland and Eire, whilst France beat Cyprus. 2010 has been just as bad, with a pathetic group stage where France finished 2nd despite being in an easy group (Serbia, Austria, Lithuania, Faroe Islands, Romania). As for the handball qualification against Eire, let's not even go down that path. Hidalgo lead the French NT in a time of no 2nd place play-offs and much smaller groups. 1978? 4 matches to qualify, against Bulgaria and Eire, winner of the group takes all. 1982? 8 matches to qualify, against Belgium, Eire, the Netherlands and Cyprus, top two qualify.
Qualification for the Euros. I only broke this away from the previous point as it was getting too long. Both managers have the same record in Euro qualifiers : 66% won, 16% drawn, 16% lost. And both faced pretty solid groups too : Domenech had freshly-crowned World Champions Italy, Hidalgo had soon-to-be 3rd in the tournament proper Czechoslovakia, Domenech had the underdog of the last world cup Ukraine, Hidalgo had not-brilliant-but-solid Sweden. In fact, they both finished 2nd in their group behind Italy and Czechoslovakia respectively. But since Hidalgo's group was only a 4-team deal, he didn't qualify. Domenech on the other hand had 7 teams in his group, so went through. The only problem is that whilst Hidalgo only had 2 "easy" matches (Luxemburg), Domenech had 6 (Faroe Islands, Georgia and Lithuania). And Domenech was super-boring with his team selection again. Sure, France scored 25 goals in 12 matches during the qualification. But 14 were in 3 matches against the Faroe and Georgia. The rest was 11 in 9. With 3 matches where France didn't score. Not terrible.
Of course, then there's the actual performance -at- the tournament (2006 is similar to 1982, except 1982 had more style and wasn't just one player running the show; 2008 is worse than 1980's non-qualification or 1978's first-round exit combined, given how badly France was spanked). Hidalgo has 1984's trophy on his mantlepiece, Domenech has diddly squat. That's a major difference.