I find 58C (136F) for 2.5+ hours to give the best results. I experimented with 60 and 62C for a little while but found that there is considerable moisture loss once you get above 60. Longer cooking times don't matter much; I've forgotten about the meat on more than one occasion and left it overnight (8-9 hours?) with no adverse impact on the final product. I personally found chicken breast after 24 hours unappealing, but my partner liked it - I would describe the texture as 70% meat, 30% cake? I would avoid shorter times though - 2.5 hours is usually well inside the safe margins for the thickness of meat I'm using according to Doug Baldwin's models.
However the biggest (positive) difference in the result has been from switching meat suppliers, and in a literally eye-opening way too: Organic chicken breast makes for a significantly nicer result every single time!
We actually did blind testing across multiple batches of meat and across several weeks, and found we could pick the organic chicken with 100% accuracy. There are differences between even organic suppliers, but in general the stringiness was gone, the meat cut in straight lines without tearing or shredding along muscle fibres, and it was noticeably more moist and juicy.
I suspect that the difference comes largely from better quality feed and the fact that the animals tend to be (at least in Australia) slower-growing breeds and ~50% older when slaughtered, thus have more time to develop more flavourful muscles.