The builtin input and sys.stdin.readline functions don’t do exactly the same thing, and which one is faster may depend on the details of exactly what you’re doing. As aruisdante commented, the difference is less in Python 3 than it was in Python 2, when the quote you provide was from, but there are still some differences.
The first difference is that input has an optional prompt parameter that will be displayed if the interpreter is running interactively. This leads to some overhead, even if the prompt is empty (the default). On the other hand, it may be faster than doing a print before each readline call, if you do want a prompt.
The next difference is that input strips off any newline from the end of the input. If you’re going to strip that anyway, it may be faster to let input do it for you, rather than doing sys.stdin.readline().strip().
A final difference is how the end of the input is indicated. input will raise an EOFError when you call it if there is no more input (stdin has been closed on the other end). sys.stdin.readline on the other hand will return an empty string at EOF, which you need to know to check for.
There’s also a third option, using the file iteration protocol on sys.stdin. This is likely to be much like calling readline, but perhaps nicer logic to it.
I suspect that while differences in performance between your various options may exist, they’re liky to be smaller than the time cost of simply reading the file from the disk (if it is large) and doing whatever you are doing with it. I suggest that you avoid the trap of premature optimization and just do what is most natural for your problem, and if the program is too slow (where “too slow” is very subjective), you do some profiling to see what is taking the most time. Don’t put a whole lot of effort into deciding between the different ways of taking input unless it actually matters.