I've not had the time to poke at either of the books — so not competent to explain/judge differences ;-)
Bill and I talked about branding a bit after my talk last year and I think we were in broad agreement — but his content background means he has a much better grasp of it at that end. Bill's a lovely chap (@writebeard on twitter) and will be happy to answer questions I'm sure. You might also find his video from this years Lean UX NYC of interest — but it's more on the content side https://vimeo.com/94016584
I'm not really a "brand" person (I'm about 50/50 dev & UX) — my talk was really more about my experiences of what worked and didn't work rather than a manifesto or process. My broad points were:
* Busting the common misconception that "branding" was just about visual aspects (logo, style guide, etc.)
* That brand was an expression/aspect of product/market fit
* That rebranding is a kind of pivot.
* The large ad agency model of how to develop brands don't work with lean startup environments coz they're used to be being brought in to sell existing products where p/m fit is, to a large extent, already set. When it comes to p/m fit the Mad Men are on the green of the 18th hole. The branding folk for startups are still driving to the golf course and think they're playing cricket.
* That there are a whole bunch of folk in the branding/marketing world who have been saying smart things about the relationship between product, market and brand — and we should be making friends with them and paying attention.
* That bringing in branding/marketing folk early on makes sense and thinking of your brand as something that evolves and needs to be tested is a sensible approach.
Like I said though. I don't class myself as an expert on the brand stuff ;-)