It's worth being very careful about these constructions.
"no evidence of a difference" is fine so long as it's proceeded with "This study found", which when studies are translated to press reports often gets dropped, especially in headlines.
On this particular issue, even the original studies often screw things up unfortunately. Frequentist statistics works very differently from people's natural intuition, and the attraction of a binary decision tool (NHST) has led to a lot of lazy thinking and sloppy science.
"no evidence of a difference" is fine so long as it's proceeded with "This study found", which when studies are translated to press reports often gets dropped, especially in headlines.