This updates your os, kernel, and all installed programs to the latest release. Your host will not do much more. Not sure if you can update php with this line , it depends how you installed your php
I had some serious issues when setting up my mail related stuff on a 7 series CentOS box. Did not play the same as a 6.x series. Not really sure what it was, and I'm not real comfortable with SystemD yet - so that was another issue. With the 6 series EOL in 2020, I figure I'll have another server before then.
Well, as with most things linux, you aren't really going to see a whole lot of new features or bells and whistles or anything. On all our systems (and we tested CentOS7 considerably for quite some time on both VPSs and dedicated boxes), CentOS 7 was noticeably faster than 6, and generally used less resources. Paired with PHP 5.6, it was definitely fast.
So are you going to notice much of a difference on a VPS for an average site? Probably not. But there's no reason not to upgrade to ver. 7.
Maybe one day they will get their version upgrades to work as well as Debian's does. With my mail setup, there is no way I'd even attempt upgrading the OS with the warnings I've read about having custom repo's, etc. causing issues. Debian never had an issues for me.