I used both at the time. I think you are overstating the difference. There wasn't as much full-on JS on the web and for all the things people normally did, FF did not struggle at all.
If Chrome had been aimed primarily at IE, they could have continued to fund Firefox, or could have worked with Mozilla to do whatever improvements they wanted. For example, if the objective had been speed, Google had so much clout with Mozilla at the time that I feel pretty certain they could have contributed to building something like v8 into Firefox.
But it wasn't about any of that. It was about owning the browser because they decided it was in their strategic interest. And that's because their business was by that point entirely funded by people's eyeballs in a browser, looking at ads.
(I would argue that Chrome was targeted primarily at IE, though.)