I don't know Laravel, but reading problems people have with unit testing it tells me there's a lot of design issues in there. I understood that those problematic features of Laravel are optional, so there's hope!
See my comparision of PhpSpec vs PhpUnit in an answer of another question: First Shot at Testing Laravel 4 apps (PHPSpec/BDD vs. PHPUnit/TDD)
I'm guessing you'll face lots of problems using PhpSpec with Laravel, and often you'll have to avoid specing Laravel specific quirks, or avoiding them (facades are optional, you can use proper dependency injection). I'd aim on having as much code as possible independent from the framework and properly unit test them. Then, you can have a thin layer of framework glue code, covered with functional or integration tests. Apply the dependency injection.
As an example taken from the land of Symfony and Doctrine, I usually don't write specs for Doctrine repositories. Well, I only expect they implement a certain interface. That's all. The rest is covered with my acceptance tests. There is no much value in verifying that repositories use query builder to produce an expected query. No point really.
Going back to the tools, I can see myself mixing different kind of testing tools for different kinds of testing:
- phpspec - unit tests - I'll write most of the tests on this level
- behat - acceptance tests
- phpunit - integration and functional tests - I'll have a small number of these, as they're fragile and slow.