Easy going advisor versus expert advisor and research experience I am fortunate to have a very nice, easy-going advisor (the last because I have seen some horrible PhD advisors). He respects me and my work (I did my master degree under his guidance). Then, I went to another university and returned to him again last year. I am a first year PhD student now. However, I have some issues regarding my research.  

First, my advisor does not know much about my area even though he's encouraging me to pursue on it. To make it clear, I can't consult him in my specific area (I do consult him on other things though).

Second, he's not aiming high (top conferences) on publications. He mainly publishes on mid/ lower mid conferences and happy with that.  

On the other hand, I have met a professor who is a big name, expert in my area, affiliated with a top university and my work is highly influenced by his research. He also seems to have a very nice personality (I have chatted with his students). I met him several time on different occasions. and he showed an interest to work together for a joint paper.

Most importantly, I believe changing university will result in a  better research experience for me. In particular, I will join a lab with different enthusiastic grad students with critical guidance unlike my current situation where it is only me and my advisor. 

About funding, I have external funding and will continue regardless where I am.
I am really wondering which path to take. I am addicted to what I am doing but need the guidance and research experience which I am greatly lacking with my current supervisor. 

Update:  

The question is: How to approach this professor for acceptance ? specially without saying anything bad about my current advisor.
How you approach the professor for acceptance would be very similar to how you speak to your current advisor (should you choose to*) about your decision:


Be objective, there is no need to mention anything about either academic in a personal way, this decision is purely one for an academic reason - you want to be 'closer' to where current active research is happening and amongst those actively involved in research in your field.
Related, be polite and direct to the point.


The fact that the professor has expressed interest in writing a paper with you is a strong indication - perhaps accept this offer and at that stage mention that you wish to pursue your research under his guidance and to work within his labs.

Once it is definite that you'd get in and although you are not obligated to explain to your current advisor, it is advisable to explain clearly and positively about the opportunity to work directly with one of the top researchers in the field - I am sure your advisor would understand.