The big advantage of the Kepler method over the wobble method is that it can detect Earthlike (in size and orbital distance) planets. The wobble method could, in principle, do this too, but our instruments aren’t anywhere near good enough to pull it off-- Mostly all we can see is “hot Jupiters”, gas giants that are very close to their parent star. Yeah, only about 1% of planets will be lined up well enough to use the Kepler method, but you can deal with that by just observing millions of stars at once (which is what Kepler does).
Well, there are two fundamental properties of the wobble: How big it is, and how long its period is. And we generally have a pretty good idea of the mass of the parent star, based on its spectral type. Given the mass of the star and the period of the orbit, you can use Kepler’s laws (actually, Newton’s form for them) to find the mean distance of the planet from the star. Given how large and hot the star is (again, known from its spectral type) and how far away the planet is, you can estimate the temperature of the planet. And based on how big the wobble is, you can estimate the mass of the planet compared to the mass of the star, though that runs into the problem that the inclination angle will also change the size of the wobble we see: What they actually measure isn’t m, but m*sin(i), where m is the mass and i is the inclination angle.
If you detect the planet through an occultation, like Kepler does, then you can learn a different set of information. You can still get the period and all that follows from that (distance and temperature). Based on how long it takes to transition from full brightness to reduced brightness, you can get the radius of the planet (you can also in principle get a lot of other information about the orbit from the shape of the dropoff, but I don’t think this has been done with planets, only with stars). You know that the inclination is very close to 90 degrees, because if it weren’t, you wouldn’t have detected it in the first place. And if the planet has an atmosphere, you can sometimes even learn something about its composition, from the light that just skims the planet and passes through that atmosphere.
In the ideal case, of course, you can detect both the wobble and an occultation. In that case, Bob’s your uncle, and you can learn pretty much everything there is to know: All of the orbital parameters, the size and mass of the planet (which pretty much tells you the composition of the planet itself), and so on.