This varies across geographies. As Guennal has said, the compensation will roughly start at the same level, but can diverge quite significantly at manager level +. In London, all major consultancies (to my knowledge) start at £40k-£45k base for pre-MBA positions and £80-90k for post-MBA positions. One area though where pay can differ significantly is bonus - while bonus might range from £6-10k+ at MBB in the first year, the comparable bonus at other firms is likely to be slightly lower.
However, some Tier 2 firms (e.g. Oliver Wyman) may pay their employees less on average than MBB, but really compensate top performers - so the best associates at Oliver Wyman might earn more than the best associates at Bain.