Usually, the principal consideration is how the browser password manager protects your secret vault on disk (and in the cloud). If it’s encrypted, where does it get the decryption material? By default, for major browsers including Chrome, Edge, and Firefox, the decryption material is stored persistently on disk, protected by some OS API (and some in the cloud). The problem is that malware running on your system can access those decryption processes as well. Additionally, without E2EE, browser password managers may not resist inspections from cloud providers.
Firefox has the option to enter a primary password on startup, which can conceptually protect against this scenario. The issue is that the Key Derivation Function (KDF) used to derive an encryption key from your password is usually weak for the consideration of slower devices, and it cannot be adjusted. It would be a step in the right direction if you used a password with entropy commensurate with the KDF function that such browser managers use. However, for Firefox, unless you look it up in the code, it’s difficult; you cannot find agreements from forums (and LLMs) about the number of iterations used for its PBKDF2 function.
On the other hand, for KeePassXC and Bitwarden, and presumably some other third-party password managers, the KDF can be adjusted, allowing you to use a more manageable password while still remaining secure. For example, Bitwarden’s forums often suggest using 4 randomly generated passphrases with the default KDF that Bitwarden employs. This is more manageable in terms of memorization, recall, and typing than the typical 6-word passphrase that is usually recommended.
The second consideration for more security-conscious individuals is: once you enter the password (or something equivalent), are your secrets stored as plaintext in memory? For Firefox, it is most likely yes. For other browsers that can be set to ask for biometric authentication, the passwords themselves are probably encrypted, but the rest of the “metadata,” such as email and the URLs/domains of the websites, is most likely unencrypted.
For third-party password managers, including Bitwarden and KeePassXC, all the information in the vaults is encrypted until you unlock it. This means the secrets you have while locked are practically invulnerable to memory dumps, app crashes that result in memory dumps, and process attachments for debugging.
How are browser password managers sometimes better than third-party password managers? They offer ease of use and the ability to autofill credentials on more sites.
TL;DR: If you can deal with the technical complexities to keep your password managers safe and accessible, third-party password managers are recommended. If not, browser password managers, when run properly, will protect you from password reuse (and credential stuffing) and help resist phishing. BUT: 1) strongest 2FA everywhere is recommended, and 2) it’s CRITICAL to stay away from malware, phishing, and scams.