Each of the password management solutions protects your passwords behind a single master password, so you only need to remember the one. That means you can devote your mental faculties to create and retain a single, memorable and complex password that can foil would-be thieves. If you use local management software without employing cloud-based syncing, the password database resides only on your computer, so a thief would need physical access to your computer to even attempt brute-forcing the database.
For added security, you could solely or additionally employ key files with the master password. Doing so makes the password impossible to guess, because no password alone would grant access to the database. The downside to key files is you need to keep the files with you anytime you require account access.
The single master password approach, however, has one potential flaw. If that password is breached, a thief has access to all your passwords and their respective account URLs. You can minimize this risk using cloud-based syncing only when necessary, choosing a long and complex password and employing key files for an additional layer of authentication. Some software, such as KeePass, optionally locks to a Windows account, so only the creating account can access the database, even with the correct password and key files. All three of the big password management utilities offer protection against brute-force attacks, such as by limiting the number of attempts that can be made per second.