Under what circumstances would we prefer the second circuit to the first?
The first version is much more straightforward in its inputs. The second version requires us to think "backwards" about the S and R inputs. How could this be better?
It depends upon what gates are available in a given circuit technology. For example, TTL gives us only the NAND gate, and we have to make other functions out of NANDs. You can make a NOR out of NANDs, but it takes three NAND gates. So the NOR version of the SR latch, implemented in TTL, takes six NAND gates, whereas the NAND version takes only two. In this situation the conversion to the NAND version is worthwhile.
You will see for many of the more complex circuits available on the chips in the lab that some of the inputs are inverted in this way. If you have the value for "foo" and it calls for "not foo", then you just need to add the inversion. But you might have the value of "not foo" equally accessible (e.g. take from a Qbar output of a flip-flop instead of the Q output), and then you can save some gates.
This consideration applies just as much to the situation where you are producing a single circuit containing these multiple components on a single chip.