The one really comparable to MBB is the Corporate Growth / Growth Strategy. In this area you will be focusing on strategy projects and commercial due diligence work. This is what Parthenon originally was. The team here will likely be made by former Parthenon people some “grabs” from MBB and Tier 2.
TSE is mostly about supporting implementation / transformation. Sometimes in a PMO setting, sometimes in a less rigid, but still structured implementation team. You won't be devising the strategy, but supporting clients in its implementation. While this is not the core of MBB, a significant of their work is done in this type of projects. You will find a lot of people with Finance, OPS and IT expertise coming from other service lines and formerly from EY (non-Parthenon).
TRS is about financial and operational restructuring. Some teams at MBB are specialized on this, but this is really a very specific practice at MBB, and more focused on the operational restructuring and respective implementation support, than on financial restructuring. People here will be coming from EY restructuring practice.
As you can see from my answer, Parthenon was originally one of this business lines, and has been incorporating other services coming from EY, thus broadening the brand reach, and trying to combine deep functional expertise in certain areas with strategic thinking.
If you plan to transition to MBB, the first option (corporate growth) is the one that is closer to the core work of MBB consultants, and as such, more likely to be recognized as equivalent to MBB experience.
