With Casper Friendly Finality Gadget, can one expect greater degrees of transaction/settlement finality over existing PoW?
Casper introduces economic finality to Ethereum. POW does not guarantee finality at all. So yes, there is guaranteed improvement in possibility of finality.
Another unique component of the way that Casper does things is that rather than consensus being by-chain as is the case with current proof of work protocols, consensus is by-block: the consensus process comes to a decision on the status of the block at each height independently of every other height. This mechanism does introduce some inefficiencies - particularly, a bet must register the validator's opinion on the block at every height rather than just the head of the chain - but it proves to be much simpler to implement strategies for consensus-by-bet in this model, and it also has the advantage that it is much more friendly to high blockchain speed: theoretically, one can even have a block time that is faster than network propagation with this model, as blocks can be produced independently of each other, though with the obvious proviso that block finalization will still take a while longer.
In by-chain consensus, one can view the consensus process as being a kind of tug-of-war between negative infinity and positive infinity at each fork, where the "status" at the fork represents the number of blocks in the longest chain on the right side minus the number of blocks on the left side:
Clients trying to determine the "correct chain" simply move forward starting from the genesis block, and at each fork go left if the status is negative and right if the status is positive. The economic incentives here are also clear: once the status goes positive, there is a strong economic pressure for it to converge to positive infinity, albeit very slowly. If the status goes negative, there is a strong economic pressure for it to converge to negative infinity.
Incidentally, note that under this framework the core idea behind the GHOST scoring rule becomes a natural generalization - instead of just counting the length of the longest chain toward the status, count every block on each side of the fork:
In by-block consensus, there is once again the tug of war, though this time the "status" is simply an arbitrary number that can be increased or decreased by certain actions connected to the protocol; at every block height, clients process the block if the status is positive and do not process the block if the status is negative. Note that even though proof of work is currently by-chain, it doesn't have to be: one can easily imagine a protocol where instead of providing a parent block, a block with a valid proof of work solution must provide a +1 or -1 vote on every block height in its history; +1 votes would be rewarded only if the block that was voted on does get processed, and -1 votes would be rewarded only if the block that was voted on does not get processed:
Of course, in proof of work such a design would not work well for one simple reason: if you have to vote on absolutely every previous height, then the amount of voting that needs to be done will increase quadratically with time and fairly quickly grind the system to a halt. With consensus-by-bet, however, because the tug of war can converge to complete finality exponentially, the voting overhead is much more tolerable.
No, you cannot reliably and objectively expect greater finality in either systems, as neither can be quantified to a degree that allows meaningful comparison.
Casper aims to provide some form of economic finality by financially punishing byzantine behaviour, while Bitcoin aims to offer probabilistic finality, making a violation of safety statistically unlikely.
Theoretically, Casper should abide to BFT guarantees and provide theoretical consistency if a supermajority is honest, but, in practice, the threshold may require 80%+ honest validators, which may be impossible to prove in a trustless manner, making 100% finality impossible.
So no quantifiable studies are available?
Not that i'm aware of. Casper should provide their finality guarantees much faster than Bitcoin (which doesn't have a mechanism that is considered "finality" other than the 6 blocks confirmations rule-of-thumb,) but neither are 100% guarantees, so I'm not sure how to quantify which provides "greater degree of finality" that holds invariant of time elapsed and is tractable & applicable in practice.