In most cases yes. If you upgrade your browser, the only thing that changes is the user agent data. The underlying device remains the same and it is this that leaks a lot of fingerprinting attributes (screen, gfx card, fonts, timezone, language, operating system, battery status, audio setup, bluetooth, installed video codecs, TCP data, IP address if static etc.).

To get a feeling for this, try: https://abrahamjuliot.github.io/creepjs/ ; https://bot.incolumitas.com/ and https://amiunique.org/fingerprint

Combined with super cookies (https://blog.mozilla.org/en/internet-culture/mozilla-explain...), that's a lot of data points to stitch together a high confidence fingerprint.

Although not perfect, FF is much better out of the box at limiting the leaks than chrome.