Last time I checked, loading local files as a new tab page required either installing a third party add-on/extension or creating your own[0] in both Firefox and Chrome.
Is that still the case? Did you find an easier option?
[0] Way easier than one would assume, you just need a manifest file next to your HTML file.
EDIT: A local web server instead of loading the HTML file directly also works and avoids the need for add-ons/extensions.
My home page is ~/home.html in all browsers. Thus it's the same in Chrome, FF, w3m, whatever. Much easier than remembering how to set bookmarks/favorites in different browsers and keep them all in sync.