Charon is 11.6% of Pluto's mass. Extrapolating that ratio to an Earth-mass planet, you get a companion about 8% more massive than Mars (0.107 Earth masses).
If we assume that 0.4 Earth masses is sufficient for a habitable world, we would either need a ratio nearly 3.5 times higher than that between Pluto and Charon, or a planet nearly 3.5 times more massive than Earth. With an Earthlike density* it would have a surface gravity of 1.52G...
*Assuming similar chemical composition, density will be higher than that of Earth due to gravitational compression.
This also has something to do with atmospheric retention and a planet's mass, but it works off of the surface temperature... somehow.
Far less frequent than air travel. Each ticket would be fantastically expensive.
Indeed, it would be far worse than air travel any way you look at it. This is spaceflight. But I think in spaceflight terms, I think it would be quite a lot easier than say, a mission to the Moon.
Assume that the two objects co-orbit with a period of around a day. This should put the distance between them as similar to the distance between Earth and GEO; this would mean both a shorter transit time and lower transit dV than that between the Earth and Moon.
Since the other body will have a substantial atmosphere, it could be used for aerobraking, both to settle into orbit and during descent.
Consider a reusable TSTO and a propellant depot. Neither of these things exist currently, but they're far closer to reality than a lot of other things- say, interstellar spaceflight, mass interplanetary transit, space colonies and soforth. Given a different path of technological development, we may have such infrastructure today- or at the very least, be seeing far more advanced developments toward it.
The TSTO ascends to orbit, with the first stage pulling an RTLS trick like SpaceX intends to do with Falcon. The second stage, which one could think of as a DC-Y ripoff, refuels at the orbital propellant depot, which is refuelled by other reusable TSTOs. This gives it enough propellant to transfer to the other planet and land there.
Assuming decent facilities on the other planet, you would then refuel there, and if you're lucky, be able to launch to orbit using the second stage only. If you're really lucky, you'll be able to complete the entire flight home with the second stage only and no refuelling. Of course, if a first stage is required, the lesser dV to launch from a less massive body would enable it to be fairly lower-performance and robust while still doing its job.
Such an arrangement would probably be more convenient in terms of inter-body travel than anything we have in the solar system, especially if infrastructure already existed on both objects. Using a Saturn V or anything like it would simply be wasteful.