If you are looking for a free software you can continue to stick with MyBB. It's really good for a free one. But if you are looking for a premium software I will recommend XenForo or Invision Power Boards.
It depends on your ability as a web developer. For instance, if you cannot operate an FTP or your hosting/internet setup won't allow fast enough uploading, then SMF and bbPress might be your best choices. However, otherwise, it seems to become a subjective thing. Nonetheless, it is true the premium brands have more knick-knacks included with less hassle.
I wouldn't say the best. Each person has there likes and dislikes about forum based software. And yet again comes down to what you need it for since each software is different and each on might not get a plugin that they needed.
The as for the owner, he/she might go with this since it's easy or can code for it. I use IPB as it's easy, admin is made very good and it has so much options plus the theme is just gets better