If you mean one of the big consulting companies, the salaries for juniors are normally quite standardized according to the grade you start at. And classification to a certain grade tends to be quite rigid too, although you can try your luck trying to influence it.
If you mean generalist consulting, at least in continental Europe, there are just 4 companies that pay really good money. It's McKinsey, Bain, BCG, Kearney. The competition to get these positions is huge.
Then you have the "mass" consulting, among others advisories within EY, PwC, Accenture, KPMG. They are much less competitive. It depends on the country and team of course but generally they don't pay well. You can end up working typical consulting hours (meaning: working a lot) and getting a salary you would get while working for a non-consulting company and sleeping in your own bed.
These companies don't normally offer much benefits for advanced degrees (at least in my country they just distinguish between candidates with B.A.s and M.A.s, a Ph.D. and everything above is treated as an M.A.).
"Consulting" is a huge industry and any generalizations are difficult. If you want to negotiate, you might have more luck at smaller consultancies.