What are the most important benefits that make you refuse your new offer and keep your current position?

It depends on you,as, when you try for a new job, no body or atleast your higher officals did not know or you do make them know about your endavors for new jobs. 

So the benefits100 % depends on you, if you get new learing platform in new job you should go there, if not you should remain on current job.

set with your manager , and explain to him you are very intersed in positon ,,team and company and you will like to contine and your company and refue this offere to continue in you comapy

and should you know your manager very well