Fingerprinting in the usual sense the term isn't about distinguishing Chrome from Firefox, it's about distinguishing user A from user B, … user X reliably in order to be able to track the user across website and navigation sessions.
Your example is unlikely to get you far.
Edit: in a quick test, I got a range between 8 and 49 in Chrome, and between 1.27 and 51 (!) on Firefox, on the same computer, the results are very noisy.
> Chrome and Firefox here are an example for "Two users who use exactly the same hardware but different software".
But it's also the most pathological example one can think of, yet the results are extremely noisy (while being very costly, which means you won't be able to make a big number of such test without dramatically affecting the user's ability to just browse your website).
Your example is unlikely to get you far.
Edit: in a quick test, I got a range between 8 and 49 in Chrome, and between 1.27 and 51 (!) on Firefox, on the same computer, the results are very noisy.