Okay, let's first check out some of the most easily accessible epic armor in The Burning Crusade right now, Season 2. How easy it is is debatable, but it's pretty easy overall. You technically don't need to group with anybody besides the forced-raids in Battlegrounds, you don't need to talk to anybody, you don't even need to really kill anybody (though you should, AFKing for the lose) to get this armor.
Let's look at Shaman armor first. I'm only going to list the especially important stats for this discussion, not the small potatoes Stamina/Intellect stuff.
On the Merciless Gladiator's Mail Armor, which is the Elemental set, we see 25 spell critical strike rating, the 8 mana regen per 5 seconds, and 37 +Damage/Healing.
On the Merciless Gladiator's Ringmail Armor, which is the Resto set, we see 26 spell critical strike rating, 7 mana regen per 5 seconds, and 70 +Healing(24 +Damage).
Shaman are in a good spot because both Elemental and Restoration tend to lean heavily toward Crit. You can argue that it isn't necessarily the best stat allocation for a Resto (and you might be right) but still, they use it, it's nice, it's dandy, it won't hurt you if you have it. Overall, there isn't a massive stat gap between these two pieces of armor, except that one obviously has more +Damage than the other. That one is for Elemental, and the other for Resto.
Let's look at those same pieces of armor in Wrath of the Lich King.
Merciless Gladiator's Mail Armor, again the Elemental set, has 25 critical strike rating, 8 mana regen per 5 seconds, and 37 spell power.
Merciless Gladiator's Ringmail Armor has 26 spell critical strike rating, 7 mana regen per 5 seconds, and... 37 spell power.
Elemental has 1 more MP5 than the Resto set, and the Resto set has 1 more crit rating than the Elemental set. The only substantial difference in this case is set bonuses if you plan to run around in your 4-piece for awhile. Elemental has the 50% change to avoid pushback while casting Lightning Bolt which will be better for soloing than a slightly shorter cooldown on Grounding Totem. Then again, they did just change the pushback mechanic. Maybe in this case, it doesn't really matter at all.
The choice is yours. In this case, it isn't very substantial. If PvP gear is what you're after, the differences are going to be minor, because the basic stats are a lot more simplified. You won't get much (if any) Spirit or Spell Hit, so you basically just need to look at the crit and spell power. On the PvP gear, at least on Season 2, the gap is almost nonexistent.
The issues we run into in the Shaman PvP gear comparison is the fact that Restoration and Elemental share more stats than some other class/spec combinations. And the whole PvP gear uses fewer stats applicable to PvE thing, of course.
Let's take a looksee at something more PvE friendly, while still being easily accessible. Let's use Tier 4, and we'll use the Druid sets this time since there's a bigger rift between Resto and Balance than Resto and Elemental.
We'll lay out the raw, basic stats for these since they change between Resto and Balance a bit more than the Shaman sets do. Right now on Live realms:
We have the Chestpiece of Malorne, the Balance set: 28 Stamina, 27 Intellect, 19 Spirit, 19 spell hit rating, 46 +Damage/Healing and three sockets (two yellow, one blue).
On the Chestguard of Malorne, the Restoration set: 28 Stamina, 29 Intellect, 25 Spirit, 88 +Healing(30 +Damage), and three sockets (two blue, one yellow).
That's a bigger gap than what we saw on the Shaman PvP gear, so it'll get the point across a little better. If you're a Moonkin, you obviously want the first one. I don't think that needs much explanation. It's better.
The difference between the Burning Crusade and Wrath versions of these sets lies only in the Spell Power, nothing else has changed. The Restoration set has 47 spell power, and the Balance set has 46.
There is almost no difference whatsoever in raw spell power between the two sets, but they still lean toward their specific specs. Restoration has more Spirit and Resto-friendly gem slots, whereas the Balance set has Spell Hit and Balance-friendly gem slots. The Restoration set pulls ahead very slightly in spell power, but the Balance set is still going to do a better job at DPS than the Resto set.
Now, it's unlikely that you'll be torn up inside about whether you should take the Resto or Balance Tier 6 Chestpieces for leveling up in Wrath, because you're probably either taking the breastplate for your main spec to help the raid you're a part of, or your off-spec breastplate is a 2nd set since you've been killing Illibeans so freaking long. However, for the sake of demonstration, let's look at some things with some more substantial stat allocation.
Thunderheart Tunic: 42 Stamina, 34 Intellect, 33 Spirit, three sockets (1 yellow, 2 blue), 117 +Healing(39 +Damage), 8 mana regen per 5 seconds.
Thunderheart Vest: 42 Stamina, 40 Intellect, 27 Spirit, three sockets (2 blue, 1 yellow), 17 spell hit rating, 25 spell crit rating, 62 +Damage/Healing.
Their Wrath counterparts are identical except for when it comes to spell power. The Restoration set trades its Healing for 62 spell power. The Balance set trades its Damage and Healing for... 62 spell power.
To sum things up: Healers will have an easier time soloing and leveling in their Healing gear, but it still isn't going to beat out the Damage-specific gear in that role. Healers, don't feel like you need to grind out gear before Wrath of the Lich King to have a good time leveling. You'll do just fine. However, if you are grinding out gear right now with the intent of leveling up in it, lean toward the DPS sets. Equivalent pieces across specs should balance out to have roughly the same amount of spell power, but the Damage sets will have all of your Hit, Crit, et cetera.
When in doubt about a specific piece of armor, get thine self to Wowhead or WoWDB.