As far as this season goes, barring West getting injured, Booker won't be any more useful than as a handcuff and even then, moreso in PPR. If you were desperate enough or in a very deep league, I suppose he could potentially end up being worth taking a flier on in PPR leagues to fill in as a flex/RB starter.
As things stand now, there's a decent chance he'll end up getting a couple catches per game and will probably bust a few loose here and there as well as getting a limited number of rushing attempts scattered in the mix as well. Think of his upside (barring an injury to West) as a poor man's version of Chris Perry in 2005. A bit more likely to take one to the house and more dangerous in the receiving game the Birds employ but a little less of a threat as an inside runner. And of course, Perry had the added benefit of being behind a one-dimensional RB in Rudi (albeit, very good at his one dimension back then) and consequently seeing more opportunities on situational passing downs.
As far as West goes, I don't expect Booker's touches to come at the expense of West getting his, and I see West being in the same ballpark of touches as he has been the past couple seasons.
If West does get injured, while Booker is likely the best guy to have as a handcuff, particularly in PPR, he's unlikely to get the lion's share of touches even in this situation. Buck knows the Eagles system, has performed consistently well for years now in it when healthy, and contrary to a previous reply, has been healthy for 2 full seasons now entering this year's camp. If West got injured, I'd venture to guess the splits would look something like:
Buck: 12-16 rushes per game, 1-2 catches per game
Booker: 5-8 rushes per game, 4-6 catches per game
Hunt: 1-2 rushes per game
With these touches, I'd project the total avg yardage to be about even at somewhere around 70 yds apiece. So again, if it's not PPR, you're looking at even production or a slight edge to Buck due to likely seeing more time in goal-line packages. With all that being said, I would probably still lean towards going with Booker over Buck in non-PPR leagues as a handcuff as his upside is significantly higher than Buck if West gets injured. It's entirely possible he ends up getting a higher percentage of rushing attempts, especially if he proves his worth and play-making ability with those attempts as the season goes on.
As for the depth chart at RB for the Birds, Moats is as good as gone, and I think Hunt is unlikely to see much time on the field at all barring multiple RB injuries though he'll probably make the roster as the 4th RB as Booker is currently slotted as the KR as well.
All of my analysis is based on PPR