I can hear a beat between two strings which I would normally adjust out - but then the tuner tells me that one string is slightly flat or sharp when played open.

Just because I can hear or see a difference - does it matter?

I'm guessing but on that one it may just be possible that both are right!

One thing you need to know is that there are various tuning systems. Your electronic tuner and your guitar are based on a tuning system known as 12-TET (12 tone equal temperament). This tuning system is a compromise where the frequency difference betwwen each note is divided equaly (others will favour one key over another).

The law of physics and harmonics do not work out like that though (blame pythagoras for this - look up his comma and circle of fifths on google) and an interval such as a perfect 5th does not exist on the TET system, it is a fraction out.

What I think you will find happens when Mooman and Peace tweak their guitars is that they are moving towards a tuning with say a pure 5th for one key. The downside is that moves like that throw other keys further off and the very reason for TET is to have everything as compromised as possible.

Well at least thats what I think - I get confused on this... Whatever, I think to some degree you can use your own judgement and go for what you prefer to hear.