I agree with AlbaHost, although I have not tried PHP7.1 and using PHP7.0 but if that's the first time update to PHP 7, you should select PHP7.1 because it has already included features of PHP 7.0. As I guess, higher version always has features of lower versions.
My opinion is you should go with 7.1 and if you are seeing your website is loading perfectly in 7.1, you can stay with that otherwise you can switch back to 7.0 itself. Because some website needs 7.0 itself. But you have mentioned here that your CMS supports the latest version, but also verify whether the templates supports 7.1 as well.
I think you should go to PHP 7.1 because it more faster. I cannot recommend you which of the two is much better because PHP 7.0 is more stable than 7.1. But I just think 7.1 is better because it is the latest.