1) A Manager level in one firm doesn't always equate to a Manager level in another. Don't be too hung up on title.. Plus make sure you understand the difference in expectation between your current level and the level being offered.
2) If the levels are the same based on your understanding/expectations of you. Try to get a deeper understanding of why you are coming in at a different level. Is it because you are too "technical" now and the Big 4 firm are suggesting one-step back to get your grounding in a "business" role for two steps forward in the future.
3) The whole thing depends on the integrity of the Partner (try to understand development/progression of individuals in the practice area you have an offer from). They could be trying to get you in as lower level as possible and charge you out for more and maximise the margin, or they could genuinely think it's best for your career/to set you up for success.
In any case, whilst finding out the answers to the above, until you have the other offer in your hand, you don't have one, so try to speed this along as quick as possible. This will put you in a better bargaining position. Don't deal in hypothetical situations.