The reasons for people I know to like Emsisoft varies between person but here's some of the common reasons.
1. Behavior Blocker. It's well-known that the Behavior Blocker in Emsisoft Anti-Malware is quite good.
2. Support. It's well-known that the support provided by Emsisoft is excellent. The response times are quite quick, they try to solve bug reports as soon as possible, they even have a forum where they provide free malware removal assistance (even if you aren't an existing customer).
3. Free services and not just paid. They have a free on-demand scanner which has a fast scanner and also contains theirs and the Bitdefender engine, not to mention the additions they work on for ransomware decryption utilities (for example).
4. Bloat-free protection. They focus on bare bone essentials like real-time, dynamic and web protection, no optimisation crap.
I don't really know of many disadvantages of them... I guess they don't provide a firewall anymore because Windows Firewall is usually sufficient and most firewalls among security software rely on the same technology as WF anyway (it just extends by using the technology to do things like additional/more extensive filtering) but for some people that can still seem as a disadvantage. They don't have a sandbox like Comodo or Qihoo either which could be seen as a disadvantage for those that like using a sandbox. I guess you have to look at your needs to decide if Emsisoft is right for you or not.
Emsisoft Anti-Malware is a good product, they provide a free 30-day trial so you can try it out and stay with them if you like them. If you don't like them then you could try something else instead. Don't use AV-C entirely to decide because the results there aren't going to be 100% 24/7, vendors have good and bad days... Emsisoft use the BD engine as well as their own anyway and they also take PUPs seriously but they let the user decide for PUP detection's or not, another advantage.
Other good products I'd say would be Kaspersky Internet Security, ESET Internet Security, or even Norton products (I like SONAR).