You have just used both different definitions of power factor.
The first, watts/(VARS + watts) assumes that VARS is the classical definition of power factor (assuming the VARS + watts is a vector sum, of course).
The second, volts * amps will differ from VARS + watts if the current measurement includes higher order harmonics.
Worry wart? I don't think so. The effects of non-linear loads, even in residential systems is quite noticeable. The last time I checked, the voltage waveform in my neighborhood was visibly flat topped. The peak was about 10V below the ideal peak voltage of a pure sine wave.
This is particularly bad for electronics equipment, since their power supplies (the cheap ones) are more sensitive to the voltage peak than the RMS value. If the supplies are regulated (constant power), they will compensate for this drop by drawing more current and this current will be drawn near the voltage waveform peak, aggravating the situation further.
EU regulations are aimed not only at correcting the 'classical' power factors, but those of the non-linear variety as well.