The biggest difference between the free version of Malwarebytes AntiMalware and most anti-virus programs (paid or free) is the operating mode.
MBaM is a scanner that runs when you choose to run it. It searches your system for malicious programs and gives you the option to remove them.
Most anti-virus programs monitor system operation while things are happen. When a file is executed, opened, or written, they scan it. If an attempt is made to create or access a file that matches the virus database, a warning is produced immediately and the access is prevented.
Each mode has its advantages and disadvantages. MBaM's passive scan mode consumes no resources when you aren't specifically scanning and it doesn't interfere with normal operation at all. However, it won't protect you from malware between scans at all. The active monitoring of anti-virus programs will catch threats much quicker. But it consumes resources at all time and can interfere with normal operation.
The general recommendation is to use scanning programs like MBaM in addition to a normal anti-virus such as Microsoft Security Essentials. The anti-virus will catch most threats immediately, and the scanner will get any that slipped through the cracks. (For example, if they weren't in the database when your computer first encountered them.)