Hi, and thanks for the question!
As the title of my answer suggests, it really is a matter of where you are at in your technical and musical abilities as to whether you use flat or rounded (on the tips) forms in thumb positions (and lower-pitched positions as well!). I advocate rounded pretty much as the BASE of your technique. There are times when a softer sound (not as focused) is desired, or for certain contortions flat fingers provide exactly what's needed. In very quick, Rabbath-like passages - say running 16th across three strings, for some people they can actually go faster using "flat" style fingering, and others are faster rounded. Flat style is where you do NOT bend any but the very first (near the tip) knuckle. There are many double stop situations, or across string "crab" technique fingerings that require at least one finger using flat style while the other are rounded.
So, it has to do with the music, the approach of the arm, and how adept you are right now. BUT the brightest, clearest sound, IMO, is with tips pushing the string to the board. Flats have more flesh between the string and the bone of your finger, so will usually sound less focused, for the same amount of energy applied downward to the board. Flats are less efficient than rounded, but are needed for many applications.
ANYONE that says either is the way to go ALWAYS has not truly thought about it, or listened very deeply the sound each approach makes.
Patrick
