Since this thread is now 5 pages long you can probably guess that there are a lot of varied opinions on the subject. I'd suggest that you read some of the stuff by Nathan Foster at ballisticstudies.com. That guy has published A LOT of stuff on tons of different bullets, calibers, cartridges.
The answer to your question really depends on how a bullet is constructed and how it is designed to perform.
In general, bullets which fragment by design typically will perform down to 1800fps, classic soft point lead/copper designs down to 2200-2400fps, and monolithic bullets ~2400fps (however to be optimally effective they need an impact velocity of 2600-2700fps).
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Bergers for instance will perform down to 1800fps. This is the speed at which the bullet will completely fragment and why they are so effective at long range. They typically transfer 100% of their energy to the target, have multiple wound channels from fragmentation, and create a large permanent wound channel even with the relatively small amount of hydrostatic shock generated at that impact velocity. The same can be said for SMK/TMK/ELDM/Amax. Barnes on the other hand don't expand well below 2400fps and furthermore in order to generate significant hydrostatic shock (critical for fast killing especially with a monolithic bullet) ideally impact velocity needs to be >2600-2700fps.
More classic designs are typically somewhere in the middle, and while not as sleek as modern long range designs something like an A-Frame/Woodleigh Weldcore/Nosler partition when used at appropriate ranges/velocities performs extremely reliably.
You also need to consider what kind of tissue damage is acceptable to you. If you're of the mindset that dead is dead then fragmenting bullets work extremely well. If you prefer less tissue damage/bloodshot meat, prefer complete pass throughs, and are better at tracking then monolithics are a better choice because comparatively they tend to have somewhat delayed killing. That being said they both are effective so long as you can put it through a vital structure.
Personally, for long range, I like a bullet that performs like a Berger, dumping everything into the animal at a relatively low impact velocity. The multiple wound channels and large permanent wound cavity make up for the lack of hydrostatic shock at that impact velocity.
However, that being said, I'd like a bullet which performs like a hybrid of the two. Dumping a ton of energy by fragmentation but then having a monolithic base which will penetrate for a pass through. That extra hole allows for much faster exsanguination. Lehigh Defense makes the monolithic Controlled Chaos and Controlled Fracturing rounds which are advertised to do just that. The downside to them is that they have a relatively low BC and so they won't work well at what are formally considered long range distances (beyond 750). Inside of that though they seem to be extremely lethal.
I know that brings up a lot of things to think about but if you want your bullets to perform as advertised then you need to think about them.
