I think the best use of stubborn troops is against knights. Almost all units of knights outside of choas knights count on a devastating charge to smash and break enemy units. Whether its Cold One Knights, Bret Grail Lances, or even Inner Circle Empire Knights, those units get a lot worse on the second round of combat. Often, if a unit can find away to stand up to the devasting charge these elite and costly units can deliver, than those cavalry units become extremely vulnerable in following rounds of combat. This, to me, is the best use of stubborn. Bait those knights into your Empire Greatswords or Black Guard, and watch your opponents face turn to dispair as he realizes his mobile strike force is going to sticking in one place next round, delivering 1 mighty S4 attack each.
on a side note, here's a couple updated pics of my initial models for the Angel's army.