My DS goes to an expeditionary learning school. I work at a school that used to be expeditionary learning but dropped the contract -- so I can see both sides of this.
On the pro side, I love the way children are encouraged to ask questions and seek answers. I love the way they study one topic in depth rather than memorizing a handful of facts about a bunch of topics. I love the committment to learning about meaningful social issues (last year they studied access to clean water around the world, this year they're studying rainforest conservation). I love how hands on it is.
On the con side, I think that reading and writing only (or primarily) about a topic that someone else chooses isn't the best way to build a passion for reading and writing -- last year my son brought home lots of books about water, but he wasn't particularly interested in water or the books. In contrast the kids at my school read and write about their own passions, which I think leads to more of an appreciation of reading and writing. I also think that sometimes ELOB doesn't lead to a high level of academic rigor. I find that sometimes teachers plan activities because they're "hands on" or "field work based" instead of because they're the best way to teach a particular concept of skill. For example, I know that last year the 3rd/4th graders started off their unit on geometry by going on a "shape walk" around the neighborhood. Although I love that they're connected to their funky urban neighborhood, I don't think that looking for squares, triangles and octagons in 4th grade is going to teach them much.
Overall, I see more that's good than bad in ELOB, or my son wouldn't be there, but I don't think it's perfect. The reading/writing issue is my biggest concern with the program.