Is it grammatically correct to use in a publication, that something is (a) 'much better' way of doing something?
Yes it is.
Writing or speaking, simple words can be much better than complex ones. They are more accessible, more readily understood, and less at risk of seeming pretentious.
There's nothing wrong, but here's what I would do:
- verbal: much better, slightly better
- written: significantly better, marginally better
Better is a comparative degree of good and best... Then why is it necessary to use much? Better says all... Then why should it be included redundantly?