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.
The question is: How to approach this professor for acceptance ? specially without saying anything bad about my current advisor.