Does it do the same thing as Malwarebytes, Is it supposed to be better than Malwarebytes?

Can you run this new program AND Malwarebyte?

Is it safe to run with Avast or other antivirus programs?

I'm sure there are many other questions, but those are a few that come to mind.

If a person thinks to try you might consider creating an image of the hard drive or creating a Restore point beforehand. Then if you find it does not live up to expectations you can correct it easily.

From the Emsisoft site
Not only does it monitor all active programs for dangerous behavior, but it also blocks malicious activities in real time. Its Behavior Blocking and Zero-Day-Attacks technology recognizes new and unknown Trojans, backdoors, keyloggers, worms, viruses, spyware, adware, and rootkits without the need of daily signature updates, protecting you long before the signature databases have been updated
So it appears to be a cure all suggesting it might be adviseable to remove your present anti virus. It should have no effect on Malwarebytes because MBAM does not run in the background but is an 'on demand' program.