Certainly a longer password with comparable or higher complexity, like your example, results in a safer password.
Though we have to say what "safe" means in this context. An attacker should not be able to brute-force the login. A long and complex password also adds to the security if an attacker would ever get their hands on the password database (if they don't store them as plain-text).
There are actually two scenarios regarding password security which are affected by the complexity and length of your password. The first one is an attacker who is only able to test against a black box, e.g. the login of a website. If your password would be too trivial like "password" then an attacker can gain easy access, even with a lot of security mechanisms in place (excluding two-factor authentication). This becomes much harder for an attacker the longer the password gets, especially since most websites limit login attempts.
The second scenario is a database breach where the attack has access to the password database. The security of your password, meaning "Is the attacker able to figure out my password?", does not only depend on you, but how the website handled all passwords. If the store them in plain-text you loose, no matter how complex they are. What is insecure, but often occurs, is simple hashing with no salt or a global salt for all accounts. In this case it helps having a complex and long password, because what the attacker does, is checking the hashes from the database against pre-computed lists of common passwords or even entire dictionaries of combinations. A long and complex password means more attempts are necessary for the attack.
A properly secured website should use a per user salt (and perhaps pepper), making rainbow-tables and dictionaries pretty much useless. This would even protect fairly simple passwords, but still the longer the better (or safer).
So the reason why you should use long and complex password is the first scenario and the second scenario in case of improper security. You can see as well, that the actual security also depends on the web-developers not just on your password.