That competitor was bought in the last couple of years and we all thought this would be our chance to go #1 as their head office inevitably screwed it up somehow.

That hasn't happened yet. They're still #1, we're still #2, and the gap hasn't closed. The only sign of trouble might be that their product, which was already lagging, hasn't seen a major release in that entire period.

I'm talking for personal experience from someone mid-career that moves around a lot in the industry.

The best buyout experiences are the slow embraces instead of a big bear hug. A slow embrace allows both sides to grow while they learn how to support each other. A big bear hug will suffocate the purchased company while all energy is spent assimilating instead of helping customers.