I've collected the data of total population, alliance population and horde population, besides paladin pop and shaman pop, from all WoW servers and from all PVE, PVP and RP servers. From all them the high lvl (55-60) and total (10-60) pop.
With this data I wanna compare differences between the server types, and confirm if it's true that paladin/shaman are overpowered and if they have advantages over other classes.
It's very important to note that this data is just a sample, so don't get it as it was all WoW population! Since I don't know what fraction this sample is of the population I'm not able to calculate variations.
I'll consider high lvl as the initial population of WoW, the people that played the most, and who is not high lvl I'll consider new players, and players with alt. It creates errors on results too.
Comparing today high lvl pop with total pop we are able to see how the server changed these 2 months.
I'll start comparing server types. PVP servers have the largest high lvl population, but now the total pop of PVE and PVP is equal, suggesting that in the begining people though PVP servers were the best and now they are migrating to PVE servers. Considering that there are more PVP servers than PVE servers, it indicates an even larger migration from PVP to PVE servers.
RP servers also increased population faster than the average.
Horde and Alliance pops should be equal, but only at PVP servers it happened, which tends to equallity. PVE servers are stabilized with 2 alliance for each horde, and RP servers have 2.5 high lvl alliance for each 1 high lvl horde and 2 alliance for each horde on total pop. It's a shame that Blizzard didn't take providences in the begining, but at least I hope that this unbalance decreses.
I though the PVE high lvl pop would be the largest, since at PVP server there is more worn-out time pvping and at RP there is more worn-out time role playing, while at PVE server pvp is much less common and role play is extremely rare.
But I was wrong, while 3.71% of total pop is high lvl, it's only 2.81% at PVE and almost 5% of PVP servers!! But high lvl pop is only 1.7% of RP servers, which means they are having fun role playing

Now, finally the differences between Alliance and Horde's difficulty of playing.
If the proportion of alliance/horde in high lvl is equal to total pop, than alliance is as difficult as horde to level up.
And look this discovery, while high lvl alliance are 3.48% of all alliance pop, horde high lvl are 4.1% of their pop! Will it be that horde is easier than alliance??
NO! I CAN'T say that. Because at PVE servers both high lvl are exactly 2.81% of their total pop, at PVP servers it's 4.58% for alliance and 5.39 for horde, and at RP servers alliance are 1.83% while horde are 1.49%. So that difference is larger only at PVP servers (wich have the largest high lvl pop), which only may suggest that alliance pvp more often than horde.
No conclusion, unfortunately.
And now comparing the paladins with the rest of alliance and shamans with the rest of horde. This is the hardest information to get, since there is not balance between classes (there are fewer priests and druids), at the same time that the choice proportion may have changed in these 2 months (I THINK that more people are playing with paladins now than in the begining).
What I did was just get the high lvl/total pop proportion for these 2 classes.
In all type of servers paladins are 17% of alliance and shamans are 16% of horde.
Also in all type of servers the high lvl paladins are 22% of high lvl alliance, should it means that few people are playing with them?
But with high lvl shamans there is difference between the servers. In the average they are 7% of high lvl pop, at PVE they are 18.6%, at PVP they are 20% and at RP they are 16.8%...
I leave for you to take your own conclusions

In my opinion I don't see in the statistics any advantage Blizzard could have done to any faction, I think they are balanced. But excluding the average of PVP servers I see a great unballance of people preferring to play with alliance and consequently a higher alliance population at almost all the servers.
Blizzard SHOULD have made anything to rebalance the pop, and now it may be harder for the horde to invade territories of the alliance.
At least it seems that inside Battlegrounds Blizzard will force to exist ballance. Let's wait and see.
For the supposed advantage for paladins and shamans I really can't confirm any.
I let here the info I got for future comparisons.
I hope it was worthy to u ^^