The problem is that the sun is at the very bottom of a very, very deep gravity well, and we're going very, very fast around it. Consider that escape velocity from the solar system here is about 40km/s. Near the sun, it's over 600km/s. Gravitationally speaking, most of the Sun's gravity well is below us.

To get to the Moon, we don't have to worry about the Sun's gravity well, and we don't even have to escape Earth's. We just need to establish orbit around Earth, and then transfer to the Moon, which is basically the same thing as going into a really elliptical orbit.

A comet is a lot harder, but a comet like 67P/Churyumov–Gerasimenko has an orbit between 5.5 and 1.2 Earth-Sun distances, so with some careful timing, it's not too costly to get into the same orbit, since that orbit isn't too wildly dissimilar from Earth's. We just need to get out of Earth's gravity well, then do some adjusting. If we wanted to rendezvous with a comet that had a similar orbit, but in a retrograde motion around the sun, it would require ridiculous amounts of fuel -- barring some amazing gravity assists.

KSP models all this pretty well. It's tough to get a close approach to Kerbol, even taking full advantage of the Oberth effect from low Kerbin orbit. Much easier to escape the Kerbol system completely. That said, it's possible to get there for relatively little delta-V, if you're willing to wait for the perfect launch window for some gravity assists. The downside is that you could have used the same gravity assists to carry a lot more mass out of the solar system completely.

The same is true with our solar system. We can get almost anywhere for not too much delta-V if we're patient, but some places will always be harder to reach than others.