It depends on what you're looking to do.
If you're looking for min-maxing your stats, you'll want to ditch either Skinning or Herbalism entirely from that list.
The passive bonuses from those professions are far below what the other professions offer.
If you plan on tanking, Mining is the only gathering profession worth anything.
Still a bit below what you can get out of the other professions, but 60 stamina from max level Mining is a very good passive bonus while being able to retain a gathering profession.
However, if you don't plan on tanking, Mining is not ideal, and unlike the other professions, you can't "switch" the bonuses per spec (like using different Dragon's Eye cuts as Jewelcrafting, for example).
In terms of Alchemy vs. Leatherworking, both offer their own unique benefits.
Alchemy will provide you with increased flask duration and effect (2x duration, and 1.5x the bonus effect).
Alchemy also provides you with the means to create said flasks (and potions that you'll inevitably use).
Even if you're forced to buy the materials raw, you'll end up saving by making them yourself rather than buying the finished product on the AH.
Additionally, as alchemy, you have the ability to learn how to transmute epic gems on a 20 hour cooldown (basically 1 a day).
Leatherworking will provide you with a unique-to-leatherworking wrist enchant, either attack power, spell power, or stamina (DPS, caster/healer, and tanking choices, respectively).
Additionally, you can make extremely cheap leg enchants for yourself only.
While they are no different than the ones that you can make for others in terms of stats, the material cost to enchant your own legs is very low comparatively.
Lastly, you can learn/make the epic leatherworking pieces in the end game which are expensive to craft but also very useful pieces to multiple class / spec combos.
In terms of money making, your best bet is going to be Jewelcrafting, Alchemy, or Inscription.
They have the items that people always come back for and need on repeated and frequent basis.
Note that Inscription will likely not be in this category in the upcoming Cataclysm expansion, as recent news has indicated that Glyphs made by Inscription will not be constantly replaced, but rather a 1-time-learned-forever-retained thing.
In terms of min-maxing stats, it's slightly dependant on your class/spec, but your best bets are Jewelcrafting, Blacksmithing (combined with Jewelcrafting), Tailoring (for casters/healers), and Engineering (for DPS classes, though the utility gain through Engineering is useful for everyone).
gaming.stackexchange.com/users/414/TheQ
Both could make you money on the AH with the right strategies.
I imagine alchemy would be easier, though, since consumables by their nature are always in demand.
That said, I don't think this question has a single right answer -- your outcome would depend on your ability to turn stuff into gold and your server's economy.
I'd make this post a community wiki.
gaming.stackexchange.com/users/1925/Adam Lear
I have an 80 resto druid and personally I'd choose Alchemy.
It would be more useful for yourself, friends, and guild because you could provide battle elixirs and pots for the group.
It also can make you plenty of money and is relatively easy/painless to level.
Especially once you get flight form because you can pick herbs while flying!
Also, herbs are everywhere, whereas skinning can only be done on certain mobs.
gaming.stackexchange.com/users/2672/Sam
I've found that Alchemy has been a great bonus for both of my druids (one Feral, one Resto/Boom).
The longer duration flasks is fantastic for raiding, but you also get a bottomless flask for use in Heroics, questing, light PvP, etc.
Flask of the North isn't as good for Feral (+40 STR) as it is for casters (+47 Spell Power), but it is still a nice bonus, and it can be used over and over.
Money is also nice from both Flasks and Transmutes.
I have one spec'ed into each.
For me, the +40 Crit from skinning would be nice on Boomkin, but I don't need it as much on Feral or Resto.
For Feral DPS (off-spec to tank), I sit at about 56% crit, and +50 Crit is ~2% additional crit.
A nice bonus, for me the extra time and contribution of Flasks is more important.
As for Herbalism, druids do have an advantage over other classes.
You don't need to change out of flight form to gather herbs, so you are able to save time mounting and dismounting at each point.
It is only a minor bonus, but I find it nice.
gaming.stackexchange.com/users/2791/Jack M.
I think skinning and leatherworking are a better combination if you are playing DPS as a Druid.
Skinning increases your crit chance, and with leatherworking you can make something for you or just sell it if you need money.
Armor kits that you can make through leatherworking are very beneficial as well for all specs.
gaming.stackexchange.com/users/None/
I'm looking for the profession that will be the best for me to have once it's developed pretty high.  As a druid will it be more beneficial to use the alchemy approach, as consumables will likely cost a lot at the AH?  Or will leatherworking make me so much money that it won't make a difference?  Alchemy seems the most useful now and in the long run, but is leatherworking a better route for the money?
Which druid profession is best in the long run: Skinning/Leatherworking or Herbalism/Alchemy?
gaming.stackexchange.com
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gaming.stackexchange.com/questions/5433
gaming.stackexchange.com/users/1705/Ryan Hayes
Alchemy would be easier, skinning and leatherworking are a better combination if playing as a druid.  One user believes alchemy to be easier, whereas another user believes that skinning and leatherworking are a better combination.
One user believes alchemy to be easier Another user believes that skinning and leatherworking are a better combination.