Usually appeals are not a good idea, but in this case it might be your best choice. It is very odd for an editor to "suggest" appeal.
Appeals can only be on the basis of procedure (not science!). The procedure says decisions are based on review by referees. Five of six referees said ...
Someone at the journal will make a judgement as to whether it is in fact an improved version of the same paper, or if enough has changed that it's a different paper.
This is a judgement that can only be made by someone in your field who understands your work. We cannot judge this, and the judgement cannot be made using some automatic rules.
If you think it ...
There are a lot of things you can do, but if you want the paper to be published by this journal, it is almost certainly necessary for you to undertake the major revision.
Refusing to revise will almost certainly result in an immediate rejection, based on the editor comments.
You can withdraw the paper and submit it elsewhere as always.
I'll note that "...