Since stateofdps hasn't been updated to summarise the early parses of the Firelands content, and raidbots only seems trackable for either the first hundred or all parses (and I'm a bit of a number cruncher with some time on my hands), thought I'd trawl through the numbers manually and give an early summary of how things are looking using the top 40 parses on a boss by boss basis. I've gone through just 25 man Normal data, and weeded out results that seem suspect. This could be due to either fight duration, healing done, or percentage healing done being unusually high and out of place, suggesting a bugged 10 man parse. Note, there haven't been enough complete Ragnaros parses to give a good idea of what's going on there at this stage. As a result, the Ragnaros results only comprise the top 10 parses of each of the 5 healing specs in the game, whereas all others comprise the top 40.
At this early stage a week into the patch, Restoration Druids seem to be on top, occupying first place in all but the Baleroc encounter, in which it occupies third position. The other 4 specs seem to fluctuate amongst the rankings on an encounter by encounter ranking, though the Holy Paladin spec seems to come out in second place at this time, and were it not for its relatively poor showing in the Beth'tilac and Rhyolith encounters, this would be more clearcut. Holy and Discipline Priests seem to excel in cerratin encounters (e.g. Holy priests do well in the Beth'tilac and Rhyolith encounters which would appear to favour AoE healing while Discipline Priests (as well as Holy Paladins) do well on Baleroc, which in turn would appear to favour single target healing ability. Restoration Shamans seem to be fairly consistently in the middle ground.
Overall healing numbers (HPS): (top 40 valid parses of each of 6 fights, top 10 of ragnaros, total: 250 parses per spec)
1) Restoration Druid: 19202.9 (100.0%)
2) Holy Paladin: 18143.8 (94.5%)
3) Discipline Priest: 16871.6 (87.9%)
4) Restoration Shaman: 16440.6 (85.6%)
5) Holy Priest: 16430.5 (85.6%)
Ragnaros 25 (HPS): Top 10 valid parses only, accuracy of results less clear as a result.
1) Restoration Druid: 10924.9 (100.0%)
2) Holy Paladin: 10909.7 (99.9%)
3) Discipline Priest: 9198.2 (84.2%)
4) Holy Priest: 8598.0 (78.7%)
5) Restoration Shaman: 6933.5 (63.5%)
These results were accurate as of July 5th, 2011.
I should add that I have no vested interest either way in these results, I just like looking behind the numbers to see what story is being told. When I heal I play a restoration druid (albeit badly) most of the time. My guild is a social one and I doubt we'll be seeing any of these guys any time soon, doesn't make me any less interested in the mechanics of raiding!