The distance some people put between these two types is surprising; especially seeing many members are still having trouble typing themselves either way. So I thought a discussion thread on the topic would be good.
The first thing to clear up is that both types are amazingly good at complex systems. And both types can approach problems logically and rationally. Both types are good at reading people also, and understanding people situations.
I mention this because people seem to draw lines between T and F in this case that may not be there (it is good to remember T and F are auxiliary functions, and many of both type's characteristics regarding people and problem solving are a result of Ne). The ENTP of course is better at taking a purely rational approach, and the ENFP is slightly better at reading people, and reads on a more personal level, but the distance between them isn't always that great. ENTPs have described people situations for me and seen things I didn't, and I have blitzed ENTPs (and INTPs) on logical and rational problems. It really depends on the person, the problem and the situation.
Writing wise and speaking wise, both have great communication skills. The ENTP is likely to be more grammatically correct though and traditional, while the ENFP will have a more free flowing style.
I've noticed recently that ENTPs tend to study Law a lot. ENFPs rarely do. Both do well in science and engineering and computer stuff. Both do well in psychology. ENFPs do better in journalism, and maybe writing (though grammatically worse, creativity seems higher).
When approaching problems ENFPs work backwards from the answer. Intuition understands the goals, and Fi combined with Ne fills out the details and breaks the problem down to first principles, or underlying truths. ie. they see the system, then pull it apart, rather than forming a picture of it from ground up. There is less direction than a rational approach, and defining new approaches is part of the process. A method that has never been used before may just appear out of thin air if it looks solid and will work. In this sense the ENFP is probably at the top of the type list when it comes to creative problem solving. Something that those more educated on types normally recognise. And "creative problem solver" is probably a better tag line or description for the type than "smiley flower child" . Apparently ENFPs were not so great at being hippies because they thought too much and disproved the idea anyway.
I'm not sure how the ENTP problem solves, because I'm not one. Some descriptions from ENTPs would be nice for comparison though.
Anyway that is a start, hope people from both sides add their thoughts to it, and clear up the misconceptions a bit. (we can discuss interpersonal and relating differences too, because ENTPs often get shafted by people's opinions in this area)