Look carefully at statistics because schools are very good at presenting them in the best light. How and why does the Grammar get the best results?
It could be simply because they attract the best pupils, who would get those results anywhere.
It could be because they have brilliant teachers, although rumour has it that some Grammar teachers aren't very good (they don't need to be in a school of motivated, well-behaved autodidacts).
It could be that pupils get good results because, if it looks like they won't, they get ruthlessly weeded out. Ask about the Grammar school's retention rate (jargon for what percentage make it through from Y12 to Y13).
It could be that the results aren't totally the work of the school - many, many students have tutors.
Again, be careful in looking at statistics. The Grammar may have a wonderful record in getting pupils in to Oxbridge/Russell Group but if they are all Arts or Humanities students then that is not much to you. What is the record (over time, one year might be a blip) in your specific subjects. Try not to generalise too much: if a Department gets most of its pupils an A grade then it does not guarantee that you will get an A grade. Conversely, if a Department never gets an A grade then you can be pretty sure that you won't either. You need a department that is capable of producing an A, and then make sure that that A is you.
Have you investigated in depth how they teach Maths? Some schools do Maths&FM at AS level in Y12 then the A2 in Y12. Some do the full AS/A2 in Maths in Y12 and then the full FM in Y13. Do you know what provision there is for STEP?
Bear in mind that many pupils find the jump from GCSE to A Level difficult. You may stuggle a little at either school until you find your feet. Some schools have tried to alleviate this by not sitting January AS modules, they take them all in the summer. Do you know both schools position on this?
I do feel that exams are very hard for your generation. In my day to get an A Grade was impressive, it meant something. Nowadays, a quarter of all results are A/A* and 12% of pupils get all three A2 at A Grade. It is much harder to stand out from the crowd now. Make sure that you have something else to add to your Personal Statement apart from exam results.
I would normally advise along the lines of carpe diem but, unless the Grammar was streets ahead of your current school (and it sounds as if it isn't, or else you wouldn't be asking), I would advise staying where you are: you know the system, the system knows you, you won't have to try to juggle two sets of friends, you are more likely to get honours (prefect, first team, lead in drama, etc) in your existing school.
Don't look at this as "a decision I might regret for the rest of my life". You are getting to the stage where your results do not depend so much on how well your school has prepared you, but on how well you manage yourself. A Level and degree grades are not so much down to good pedagogy by teachers but, instead, dedicated learning by students.
HTH and do come back to MN again: there are some people on here who are very knowledgeable on education.
Good luck with the rest of the exams.