Which is faster? Straight PHP With any framework there is overhead.
If Yii1.1 is fast enough for your needs, then framework overhead is not a problem. Yii2 "may" be a little faster because of the name spacing that seems to load only the required objects for that page, not every object in components/extensions/modules/etc.
Another thought would be that Yii1 is only in maintenance. Yii2 is actively being updated (read fixing problems/enhancing). I would probably go with the upgrade to Yii2. It also provides for the cleanup/optimization of your code. Let’s face it, you know more now than you did before, you may know a better way of doing X than you did when you wrote doing X.
Just random thoughts. Good luck.
p.s. Looking at the first file of the link component, It doesn’t look like a lot of “Yii code” in there, so there may not be too much difference.