I don't see how data only on the competitor would be any more use than data only on Firefox. Ideally, you'd want both, but with that not possible, data on just Firefox is pretty good too.
The question of why people are leaving Firefox just boils down to why people don't like Firefox, and the imagination runs wild thinking about ways these metrics would help answer that question.
About the most basic thing I can think of: if stats show half of the features you have developed are never used, you can assume that's part of why users leave Firefox. Competitors, who have market intelligence, are spending all their development money on features users want and Firefox is spending 50% of it on features they don't.
Or, over time, you see most of Firefox's decline is in uses on old computers. So maybe it's because the competitors are more backward compatible. Or maybe it's harder to install on a new computer.
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