Choose the project that gives you stronger evidence of problem solving, ownership, and impact rather than choosing based only on whether the word 'strategy' appears in the project description.

MBB recruiters will care about what you actually did. Client implementation can be highly relevant if you diagnosed problems, worked with senior stakeholders, and drove measurable results. Internal strategy can also be strong if the work is analytical and consequential.

A client implementation project where you redesign a process and deliver a measurable cost reduction may create a stronger story than an internal strategy project where your contribution is limited to research and slides.

Compare the two roles on ownership, analytical depth, client or leadership exposure, and measurable impact. Pick the one that is most likely to give you strong stories rather than the one with the most consulting-like label. If useful, this guide on MBB vs. Big 4 gives more detail.

I'd take the project with actual ownership and measurable impact, even if it's implementation.

client exposure can be a stronger story than internal 'strategy' work.