I don't recommend using its browser add-on though, so this only fixes your case if you have two (or more) devices to use that will be active at the same time, so that any one (all but one) can die.
Also, have multiple forms of 2FA (as in any one may be used) such as a FIDO key or printed codes.
And then when 1Password released their 1Password X system which works via a browser extension that works really nicely across Windows/Mac/Linux/iOS/etc, I switched from BitWarden back to 1Password again. (caveat: I haven’t actually tested the chrome extension myself; only the firefox and safari ones)
RE: BitWarden vs 1Password, they’re pretty similar in most respects. 1Password is arguably more polished (especially in the native OS X app), and has support for storing multiple separate vaults of data (a feature which I don’t actually use). BitWarden has the ability to self-host the server (which I’ve never done, but I very much appreciated that it was an option), and 1Password historically let you just sync your vault file however you wanted to; I had mine in a Dropbox folder to share between computers, for a while, and it worked great. But now with 1Password X, they want you to use their servers. Which obvs is less great, but.. I’m willing to put up with it, personally. (I mean, I was doing the same with LastPass and BitWarden already, anyway).
For me, the big killer feature for 1Password is that it can handle “Authenticator” features; scan the QR code into 1Password and it’ll handle the TOTP code for 2FA in addition to your username/password, etc. It’s so much nicer to have it all integrated together in a single flow than to need to find my phone and launch Authy separately every time I want to log into a web site.
I use one of these https://www.yubico.com/product/security-key-by-yubico/
The keys are generated by the service and you must make a note of them ahead of time. And keep them secure obviously. You get about 10 possible keys from GitHub iirc.
Also, some services (Google, apple) allow you to perform 2FA over multiple options like one of TOTP, phone call, SMS or other device interaction (in apple's case).
So if the device gets bricked, find a cheap replacement and Bob's your auntie.
Some apps also let you export the token (but definitely not Google Authenticator, that app's data doesn't even get backed up).
So I keep a spare phone at home i my safe with google auth setup. Just in case my primary is lost or stolen.