A combination of both. Most people don't understand exactly how evolution works. In a nutshell, everything mutates through time. Most mutations are not beneficial and are in fact harmful so the organism dies. Some mutations are benign and confer no advantage so continue on with the critter but there is no outward change.
Sometimes however, a mutation comes along that gives the critter a huge advantage over other critters of the same type (in other words they are vying for the same food source as an example) because it is so much better at doing whatever it is that needs to be done it is able to reproduce better and thus it's genes are transmitted along to the next generation which further distances itself from the competition.
In some cases the benefits are so great that the opposing critters actually die out completely. The competition between Neanderthal and Homo Saiens is an example of that.
We reproduced faster than Neanderthal and that is what probably gave us an edge over them and is why they eventually disappeared. They actually were stronger and more robust than we were but their gestation time was according to one theorist up to a year. There is of course some debate on that hypothesis, but if true is the only real advantage I can come up with for us vs them.
