For MBB, definitely focus on interviewee-led cases. Not really sure whether they are "harder", but the key is to come up with the initial structure.
The structure has to serve two purposes:
1. It has to answer the question.
Many candidates forget this and come up with a structure that tries to do everything, or a framework like Porter's 5 forces. For example, if you're asked for profitability, your structure should lead to profit numbers. If you are asked how to enter a market, don't answer if it makes sense or not, but how to do it. Semantics are important, so listen carefully to the case question.
2. It has to be the guideline or plan for the interview.
If in the structure you say "I focus on issues A, B, and C" - you then should start with A, finish it, go to B, finish it, continue to C, and when you finish it, the case question should be answered (see 1). If this sounds trivial, it's not... :) Some candidates come up with good structures, but then fail to follow them.
Finally, the structure should be MECE (mutually exclusive, collectively exhaustive -> look it up if you have never heard it before) and your wording should be adapted to the specific case at hand as much as possible (no "standard" framework, try to use industry- or business-specific language instead and no general business terms, e.g., for a hotel, talk about rooms instead of general "products").
Overall, I found there to be 7 general types of cases, and over time found good initial structures on how to tackle them. See my other preplounge answers if you're interested to learn more.
All the best for your interviews!