Unlike his special character counterparts Ulrik isn't that expensive when compared to the non-special equivalent, the wolf priest. A standard priest with no equipment is 100pts and Ulrik is 180pts. So why should you spend those extra points?
In terms of basic stats he isn't a huge improvement but there are some key benefits. He's got better WS and BS, an extra wound and higher initiative. The WS/BS aren't really significant as you aren't going to be doing much shooting and you're still probably hitting on 3+ in combat against most things. However, the extra wound is handy and I5 means you'll get those power weapon hits in before most things out there get to hit back. Bear in mind you're still vulnerable to instant death but since he's always going to be in a squad you can assign the hits elsewhere.
As I've mentioned he's got a nice power weapon hitting at I5 and a plasma pistol which isn't essential (I'd never give one to a wolf priest for example) but it does mean you might soften up marine squads or maybe blow up a transport before charging it's occupants. Uniquely Ulrik doesn't have a saga like the other characters but since there's only a couple of decent ones it isn't really an issue. Essentially his special rules are equivalent to saga of the beastslayer. As with the other special characters the main benefits come when you put them into a squad.
Ulrik and his squad can re-roll to hit AND to wound when in combat with a model with toughness 5 or more. This really comes into it's own against monstrous creatures such as Nids and Daemons. In my recent battle report Ulrik and his squad of grey hunters made mincemeat of a trygon prime without breaking a sweat. This rule also applies to models which are toughness 5 thanks to a bonus (such as being on a bike) so it isn't as limited as you might think. In practice, however, you'll be lucky if you get to make use of this rule as anyone who knows about it will try and keep their creatures/characters away from him. I actually prefer the standard wolf priest's ability to pick which unit type he gets Preferred Enemy for, even though this doesn't allow wounds to be re-rolled.
The mentor special rule is a nice touch. At first it may not seem all that useful but I like to use it on Lone Wolves, Dreadnoughts and even on power fist Wolf Guard in order to make the most of their limited attacks. Ulrik's other special rule, Wolf Helm of Russ is like Saga of Majesty but works for any units with line of sight to him. In addition, it means ICs wishing to assign attacks to him in combat will need to take a leadership test. This situation is pretty rare though and with most ICs having high leadership it's rarely useful. The morale re-roll is the real benefit here.
Finally, like other Wolf Priests, Ulrik get's a 4+ invulnerable save and makes his unit fearless which can be useful since Space Wolves don't have a brilliant Ld value for the most part. Speaking of Wolf Priests let's compare the points. To get a similarly equipped Wolf Priest with Plasma Pistol, Wolftooth Necklace and a Saga you're looking at 145pts. Granted you'd rarely take the pistol but the rest is reasonable so let's say 135pts. That extra 45 could buy you three grey hunters or a transport but I'd say spend it on Ulrik. He brings a bit of interest to your lists. Use him in a transport with some grey hunters and charge him towards something juicy. Ragnar probably does the job better but at 240pts you're losing something else in your list to take him. I also quite like the Ulrik model even though it's an original model thats been around a long time.
We're nearing the end of this series but there's one character left and he's a totally different prospect to any of the others. Next time it's Canis!
PS I'm going to cover Lukas and Arjac in a post together as they're upgrade characters rather than fully fledged special HQ choices.