I think the fact that you can't tell -- even if the answer really is that there is no particular order involved -- suggests an issue with the storytelling.
Both dungeons are just clues as to what is to come with the coming expansion. You can do them in either order, but unlike last year's Dungeon DLC kickstarting the Dragon storyline, the NPC's are not the same in both dungeons.
Thanks for all the input We ended up doing Icereach first. You are right, they're very different and it was fun doing them normal just to loot everything and follow the quest. We trio'ed seeing as we wanted to take our time. Only Unhallowed gave us one spot of bother with 2 DD's and a healer.