Normally you should test these frameworks to see which one do you feel more comfortable with, or more efficient.

To me, I don't really like your 2nd approach. You have 7 strategiess: 1. New market 2. Improve distribution channel 3.New / improve products 4. Change price 5. Improve marketing & sales 6. M&A 7. JV.

This is a lot, and it isn't MECE as well, probably there are more ways to grow. But the big question is How would you really start/prioritize the case after saying this framework? My hypothesis that you'll based on your real experiences about different industries and prioritize the 7 strats differently. But I think industry experiences aren't valued in case interview.

I would prefer gathering datas first, then based on that create hypothesises. For the growth case, I prefer identifying the potential sources of growth before thinking about potential ways to grow.

Let me try combining your two mentioned frameworks into one.

In order to help the client grow the revenue by X% in Y years, I would like to look at:
1. Customer 2. Product 3. Company 4. Competition

1. Customer:
I would first want to have more insights about the customers by looking at. a. Who are they and what are their preferences? b. How big each customer groups are in term of revenue potential and their potential growth? and c. Our market shares in each customer group.

My goal in analyzing the customers is to figure out if we can a identify a new fast growing customer segment (1.New market), or if the growth is not very attractive, we can try growing in the segment that our client have the least share in (This can be 2. improve distribution, 5. improve marketing, or improve blah blah...)

2. Product
In term of the product, I would like to consider: a. Existing proucts b. New products.
For existing products, I want to understand 1. characteristics 2. pricing 3. marketing 4. distribution 5. compare all that with customer preferences to see is there any opportunity for us to grow existing products by either selling it to existing customers or potential new customers.

3. Competition
a. Competitor in diferent segments (share, strength, weakness, their reaction)
b. Potential M&A opportunities

4. Company
a. Capacity & operation. (Is our growth surpressed by capacity & operation constraints? Do we have the required capacity for growth?...)
b. Cost structure (What is our current cost structure? Can we reduce the price to improve revenue?...)