In practice, there seems to be no difference.
As I understand it, most people and IDE implementations prefer to instantiate with parentheses to follow the code standard used in the PHP documentation itself and by the community in general, which follows that of other languages objects.
I did not find a reference in the PHP documentation, only one in the Wikipedia that says:
Function calls must have a parenthesis, except for the class constructor function when it has no arguments and is called with the new
of PHP operator, where the parentheses are optional (free translation) .
Someone can argue that saving the two characters (2 bytes if using ASCII encoding, 4 if it's a UTF-8, ...) your PHP file would be loaded and interpreted faster. However, any gain is likely to be insignificant and unmeasurable, since PHP files are always full of "surplus" characters, especially when mixed with HTML.