To be honest I'm not very enthused about the way linear types are being added to Haskell. I think linear logic has a lot of potential to drastically change the way we approach programming and I'm not so interested in marginal improvements to current languages. I really like this paper [0] as an example of where we could be going. Note that the author is also part of the initiative to add linear types to GHC.

[0] http://assert-false.net/arnaud/papers/A%20dissection%20of%20...

What’s the essential difference between the approach described in the linked paper, and the one Haskell is taking? And what makes you favor the former?

In System L the evaluation contexts are first class and treated symmetrically with values. This goes beyond the functional paradigm. The Haskell proposal seeks to implement functional aspect of linear logic.