I suggest CentOS 7. In fact always go with the latest stable to avoid immeediate upgrade later on. Like for an upgrade from CentOS 6 to 7 later, you will have to do complete system wipe or a new server because direct OS upgrade is not possible with 6. New version comes with new features, reports says more memory efficient, booting is fast, systemd brings in lot of features, new firewall [ optional ] , etc etc...If you are planning to install any control panel over it, yes CentOS 7 with no doubt.
At start I also not liked the centos 7 due to firewall and some other changes, but the thing is latest version is always better. Within some years the centos 6 will discontinue and you will again move to centos 7, so why dont move today.
No doubt it is CentOS 7x, it has been released in 2014 and since then it is have been further developed. it makes sense to use older versions only for clients whop have specific software which has not been updated and who (for various reasons) cannot use version 7.
To avoid any issues when moving from CentOS6 to CentOS7 choice in my opinion would be CentOS7. If not mistaken, CentOS6 will not be supportable with even security updates after 2020 November, which is not too far away.