Dawn orbits Ceres at thousands of kilometers periapsis altitude, and doesn't seem to plan to go lower than 375 km. In contrast, Rosetta has been down to about 30 km altitude, and will finally even try to soft-land. And that's at a comet with a coma that might already have caused Rosetta to enter safe mode as its star tracker confused debris around it for stars.
Is it maybe because of gravity, propulsion, instrumentation or spacecraft design? Isn't closer better?
Much, much higher specific orbital energy ($\epsilon$) and Dawn's lack of high impulse thrusters. OK, technically Dawn has 12 x off-axis 0.9 N RCS thrusters, but it only launched with 46 kg of hydrazine for them, so it pretty much depends on its three 90 mN ion thrusters alone. See this answer for more detailed explanation of its propulsive systems and limitations of low thrust propulsion.
As for $\epsilon$, rough calculation for Rosetta's 30 km orbit around 67P/Churyumov–Gerasimenko gives me ~ $-0.01\mathrm{\ m^2s^{-2}}$ (note that 67P is a highly irregular body) and for Dawn in 375 km orbit around Ceres $-37,364\mathrm{\ m^2s^{-2}}$. That's a huge difference of a few orders of magnitude and where the amplitude of required energy to do corrective orbital maneuvers comes from (multiplied with the mass of the orbiter to get required energy in Joules, but Rosetta and Dawn have roughly the same mass by now), should those be necessary, say due to mascons (mass concentrations) and otherwise uneven gravity field or even presence of surface outgassed (or ejected in Ceres' case since it's suspected to be a geothermally active body with cryogeysers of salt water as one possible explanation for those infamous white spots) materials increasing density of the medium it has to orbit through (and thus influencing orbital decay).
Rosetta doesn't have these problems, because it will end its (primary) mission by the time it runs out of propellants and it requires a great deal less of them and much shorter bursts to maintain its quasi-orbit around 67P. Quasi because it's constantly maintained with impulse burns and would not stay in even close to desired one by the time it takes it to complete one single orbit around the comet without them. I can't find a good info on Rosetta's current orbital period, but it should be roughly 16 days, ± quite a bit due to all the uncertainties. Luckily, from observational and Philae lander's perspective, the comet rotates much faster on its own axis (12.4 hours). Still, perhaps a better term would be that Rosetta is station-keeping around 67P than orbiting it?
Note also that a 375 km orbit around Ceres takes ~ 320 minutes, while a 30 km one less than half that at ~ 145 minutes. Perturbations, both by nodal precession since Ceres isn't exactly a spherical body either, and possible mascons would mean that it would have (bigger at least) problems maintaining nadir-fixed attitude for observations, and orbital speed would increase from about 273 m/s to roughly 356 m/s. I'll let you calculate relative velocity to the ground, but as you can see, you might have a lot less time to point towards a single area in a single pass and it would reduce in size too, since angular resolution of your instruments remains fixed. This is especially important for observations of Ceres on its night side, with required long exposure times.
There's another point to keeping Dawn's final orbit relatively high. I can't provide a reference because I don't remember where I heard this (could have been during some lecture, press conference, or Dawn's blog - I will update when I find it), but unless I remember it wrong, plan for Dawn after completing its primary mission and once it runs out of propellants / reaction mass is to simply leave in orbit around Ceres, and the word was (wherever I remember this from) that is should stay there and be able to return science data for quite a while longer. Of course, if you placed it in an even lower final LAMO (low-altitude mapping orbit) before burnout to dry, its orbit would precess much faster to its final lithobraking demise as a small, fan-like debris field on Ceres' surface. Maybe that's what those bright spots are? Or graveyards of disco balls from the 60-80's? Joking aside, since it's solar powered, there's no reason why most of its instrumentation couldn't operate for many more years to come. In its environment, assuming no astronomical event, it should only lose about 1% of its power per year. And while at least one of its flywheels still functions, it should be able to maintain periodic contact with Earth.
Conversely, while that is true also for Rosetta, the comet chasing probe can't orbit 67P for very long before its orbit is perturbed too much by comet's uneven gravity field and gravitational attraction of other Solar system bodies during perihelion and close approaches at not too big of an inclination to the invariable plane (~ 7°), and either crashed into the comet ungracefully or nudged far away from it never to return anywhere close.
