A password manager and a simple encrypted database/textfile/whatever is roughly equivalent for threats which are most relevant to the average user (assuming the encryption was done decently, e.g. using a sufficiently slow method): attacks based on password reuse (ie. someone sets up a honeypot website or breaks a weakly guarded site and tests the collected usernames+passwords against gmail) and low password enthropy (ie. the password can be guessed by generating a huge list of password-like strings and trying every one of them).
The big difference is against threats where your computer is partially compromised: for example, someone installs a keylogger (good password managers can auto-type using a mix of copy-paste actions and simulated keypresses which makes it hard to log), or they spray liquid nitrogen on your computer and rip out the memory chips while you are on the toilet (good password managers avoid keeping unencrypted copies of the passwords in memory).
All in all, if there is no strong reason against it, you should use a proper password manager such as KeePass (or OnePass or LastPass). If you find some other random password generation + encrypted storage method fits your workflow better / is easier to explain to your grandma, use that and don't worry about it too much. Stealing your password from one site and reusing it at another has a fairly high chance of happening, while getting infected with a keylogger is much less likely if you use an antivirus and common sense (and if you do get infected, passwords won't be your biggest problem - it will be credit cards or identity theft).