Post by Sinespe
Many of the answers here refer to healing. On that subject, since so much has been covered, I will just add that there is a Discipline module of Recount
available to estimate the amount of absorption that a Disco Priest -- this module was created by the maintainer of the Recount addon, so it is very reliable in terms of interaction with the rest of the mod.
On the subject of DPS, all I can really do is link you to certain World of Logs parses that include my Alliance Priest within them. My guild does Ulduar-10 exclusively, and we are working on Hard Modes slowly but surely. I can reliably be said to have either an Elemental Shaman or a +13% Spell Damage buff at all times, so take that into account when measuring my DPS against that of your own Shadow Priests. As a benchmark, if they're able, on their own steam, to put out about 2.6K DPS on the Heroic Training Dummy in Naxx epics, then they're doing a good job in terms of rotation. How that translates into Ulduar fights, of course, is much different, because there are very few Stand-and-nuke fights. However, a good knowledge of rotation is generally the basis for a good understanding of how to put out the highest DPS possible while still moving out of the fire.
So, without further ado, a few benchmarks for you. Be aware that I do also include Naxxramas runs, because some of the fights in there are still excellent tests of DPS even if you're in Ulduar. Additionaly, I link to "Total damage done on successful boss kills", rather than a full report, because bosses are all that matter. Trash is not important, for the most part. Do explore them deeper and more specifically at your leisure.Ulduar-10Naxxramas-25Naxxramas-10
I trust that this helps you, and I wish your raiding group success in their endeavours!