What are the pros and cons of choosing my own research topic?

(This question is one of three correlated questions: Can I get enough help? (first part), How should I do it? (second part).This is the third part.)

I am an undergraduate student (in Computer Science and Engineering) and I will be starting undergraduate research for my thesis. I have talked with many professors about possible projects and all the projects they proposed to me seemed interesting enough.

During summer, though, I read a paper and I was very interested and excited about it, but this paper was not for the projects that were proposed to me, but in a different area. I would like to do research in this area but I have some questions, because none of my professor is doing research in this particular field.

So, my questions are:

1. 
   

   What are the downsides of choosing my own project instead of doing a project that a professor is working right now (with his Ph.D. students)?

   
   


2. 
   

   How harder will it be to get something good out of it (in comparison with doing a proposed project)?

   
   

P.S. I want to understand whether it will be beneficial to do a project that I want to do because of some paper(s) that I read or it will be better to do a project that was proposed to me. Also, I would like to go for a Ph.D. after I graduate.