Well, first of all, you'd run into the chicken and egg problem. How do you fill a competitor with data without blatantly copying Wikipedia's data? How do you fill in data without editors? How do you get editors without data? It's not unsolvable, but a very tricky problem.

Second, you'd have to overcome Wikipedia's massive marketing efforts, particularly with the word "wiki". People often use the term "wiki" as a verb in the same way they use "google" as a verb. How do you get people to think "I'll look that up on Clonopedia" instead of "I'll look that up on Wikipedia"? It's not insurmountable, but potentially a very, very expensive proposition.

Third, despite Wikipedia's flaws, it is really one of the best collections of knowledge on the internet. It's so vast that the editing has slowed down because everything goes on there. This is like winning an architecture competition where they submit the Taj Mahal and you submit a sandcastle. It's not impossible, but... well... good luck.

That said, I would enjoy some serious competition for Wikipedia and similarly placed entities (Google, etc).