If you are in federal consulting, then expect coming in at a higher level or jumping to a better company. The pay difference between the degrees is massive, assuming you go to a top 25 MBA program (95-110k + a signing bonus vs. 65-70k at a good MPP program).
If you are not in the federal consulting business but want to get into it, a dual degree would certainly help but you can prob get by just one of either. The hard part of the MPP is getting into a job with real policy work (assuming then you don't want federal consulting). While many people go to think tanks and NGOs, you will need to make sure that your school places people at the types of Agencies where you want to work (Labor, DoD, State etc.) if you want federal work over thinktanks.
However, its important to note that going into the private sector, federal consulting aside, with an MPP is hard. If you have 6 years of WE by the time you apply, you should be a sitting pretty for many MPPs if not MPAs. That said, this is a #s game so a respectable GRE is important.