This topic has already been covered extensively on MMO Champion or World of Raids when the blues gave us details on it. And I wasn't really going to talk about it but well, if it can be useful, here is my share on it.
First, how do you get Val'anyr ?
You have to collect 30 Shattered Fragments of Val'nyr. Then you'll get a quest, and you have to beat Yogg-saron in heroic difficulty with at least one of the watchers not assisting you (that is not an easy task).
Now, beside its amazing stats, we'll discuss here about its equiped effect.
Your healing spells have a chance to cause Blessing of Ancient Kings for 15 seconds allowing your heals to shield the target absorbing damage equal to 15% of the amount healed.I will add information from blues.
The proc is 10% on any direct heal or hot tic (it is not clear yet if a Judgement of the Light proc will make it proc or not and I think it probably doesn't proc on a glyph of Holy Light splash heal) that does not result in 100% overheal (it has to heal at least 1 hp).
If the proc happens, you get a buff for 15s. During these 15s, each healing spell you cast will proc a 8 seconds duration shield on the target which will absorb up to 15% of the full value of the heal you just cast. If you cast other heals on the same target, they will renew the duration of the shield and stack up to 20000 damage absorbed.
Now that we have identified the shield effect and how it works, the big question asked is: which class would benefit the most of this effect?
We have to consider two aspects: the chance of activating the effect, the power of the shields given.
Blessing activation chance
It's a flat 10% on any direct heal or hot tick. Let us see what is means for a paladin.
A paladin roughly cast a spell each 2s, considering Holy Lights, Flash of Light and Holy Shock and movement. That's about 30 direct heals a minute, about 3 procs a minute, the blessing lasts 15s. It shows that we would be mostly 75% of the time under it's effect if we could have it proc as soon as it's down, which will not happen. We have to consider that healing while under the blessing will not proc it again.
So it's mostly the time need to proc it between each of the blessings. 10% proc chance means you need about 10 heals or hot ticks to proc it. That's 20s for a paladin, that will be nearly instant for a healing druid with hots already ticking all around.
I am assuming here that the blessing proc can't happen on Judgement of Light, or that, as a good holy paladin, you're judging wisdom if there is a protection or retribution paladin in your raid.
Now, how much shield can be generated in 15s ? With a full Light's Grace active and haste buffs, I'll count 1.5s casts for Holy Lights. On my wss parses, they are around 12K medium (counting crits). That will result in 120K healing with the buff, giving us a total 18K shield. Still not the 20K limit but definitely something good. Add to that the shields will have "proced" on anyone not being full life and hit by a glyph of Holy Light splash heal.
If we consider what most other healers will do in 15s it's probably less than 120K healing. Or at least not without some serious mana issues. Without cooldowns, these 10 Holy Lights cost 12740 mana. With the Libram of Renewal, it's 1130 less mana. With 50% crit and Illumination it's 3822 less mana for 7788 mana total. (I'm not taking into account things like Glpyh of Seal of Wisdom, which reduces these costs by 5% more). With a 15s duration and 20s between blessings, that's about two times this "crazy heals" by minute, hence a little more than 15K mana a minute, which is a lot even for a Holy Paladin. Using Divine Plea will be necessary for about 6K mana each minute, reducing the cost to 9K mana (though you have to continue outputing Flash heals during the off-blessing time). With our other coold down abilities, we should be able to go crazy on Val'anyr shield for 3 to 4 minutes, resulting in 6 to 8 full shields of 18K strength. I think all people on Mimiron right now can see the use of such crazy healing periods.
To resume things
A hot class or aoe healing class will have the blessing up nearly all the time, while a direct single target healing class like a paladin won't (unless Judgement of Light counts, but that would be bad style as a Holy Paladin Judgement of Light is weaker than the one of other paladins).
But a paladin will most probably outputs much bigger shields and can go crazy if needed for a few minutes resulting in nearly capping the shield potential during that time. From my rough calculations, we can expect 18K shields two times a minute for 3 to 4 minutes from a Holy Paladin. That being for a moderately itemized Holy Paladin (like myself in tier 7 raid 25 gear), and without special mana regen abilites used but the regular talent ones.
Similar analysis for druids and priests (both disc & holy) would be necessary to compare the numbers, but I feel confident in saying that Val'anyr will be more effective in the hands of a Holy Paladin.
Now, for your raid, I say: give it to your most reliable healer, the one that is in your guild for years and is always here when you need him/her :P