This of course is it's ability to be installed and used on a previously infected computer. Malwarebytes
(if you accept the use of a free trial - this is not available on free version) can prevent termination of it's processes, and its cleaning up with something called Chameleon. This is not available for free version according to the free vs paid chart found here:
What's the difference between the M...
I find Malwarebytes is more accurate (finds threats with less or fewer false positives than Emsisoft) and more efficient removal especially if you use the premium version (which is not being compared as you are looking for free - just being through). For that reason alone, I recommend Malwarebytes Free over Emsisoft Emergency Kit if you MUST have one over the other. I would consider using both. They work well together.
Other benefits for Emsisoft: Portable (USB friendly unlike Malwarebytes), has more tools (for both novice and experienced users for free without any extra download), more engines can sometimes means more threats found - both Emsisoft and Bitdefender are very capable. Malwarebytes is focused on the newest threats rather than older ones and new - this can be both a disadvantage and advantage for Emsisoft. For me, the scanning speed for full USB/HDD/SSD is faster.
Other benefits for Malwarebytes: Emsisoft believe in prevention (preventing threats from entering the system rather than cleaning up the aftermath) which can be a reason to believe they are not as focused as others with removal of active (or inactive, remnants of (as in files that pose no threat to the system unless executed - some are simply not executable)) threats as Malwarebytes. Malwarebytes is significantly smaller in size compared to Emsisoft Emergency Kit - shouldn't matter with good download speed and having no data limit - just something to keep in mind. Malwarebytes will probably have definitions and more successful at removal for very new threats.
Both have custom scan on free version. Malwarebytes Hyper scan (looks in active memory, directories, etc for active threats) with paid only - keep in mind you can achieve the same using custom scan. EEK has quick (active threats and it's traces) and Malware Scan (typical places that malware hides). Custom can be used for full scans. Use Direct Disk Access to scan for rootkits only, not entire drives - I've had a crash using this for what it is not intended for.