After your primary ferment was over you racked all of the heavy lees should be discarded. By chance did you smell them or detect any off flavours. If you did I would recommend you go with the second racking if not I would stay on those lees to improve mouthfeel, complexity, and decrease movements with a delicate wine.
Staves give a richer flavour profile than chips and are easier to deal with as well. If you have multiple carboys or demijohns then a program could be set up where a fraction of them get oaked or oaked heavily and others dont -- giving you more flexibility and options (ie blending) for the finished wine.
I am curious as to the particulars on the grapes you started with in terms of condition (if the grapes werent in the best condition I would recommend the second racking), pH, Brix, TA. If you have them?