It's probably best to think of the 60Da as special-purpose astrophotography gear. In order to get the increased Hα sensitivity, Canon have modified the IR-cut filter that sits in front of the sensor, letting in quite a bit more light in the near-visible IR range. You can't see that light, but the camera can. For day-to-day photography, then, you'd need to add an IR-cut filter to your lenses—or you'll wind up with the same sort of problems that Leica M8 shooters had. "Blacks", in particular, will show up as various shades of magenta and brown, but the IR false colour can significantly contaminate other colours as well.
(There is, apparently, a body-mounted IR-cut filter on the market, similar to that used in the Sigma SD1 Merrill, but it is incompatible with EF-S lenses.)
On the other hand, you can't achieve the same results for astrophotography using a normal 60D and a filter. Since the sensor-mounted IR-cut filter reduces the camera's sensitivity to hydrogen-alpha (and similar wavelengths), you would need to reduce the sensitivity to other wavelengths to a similar degree using an IR-pass filter. That will mean that you'd need to increase exposure times considerably or bump up the ISO by several stops. You can correct the exposure time problem (to a degree) using a tracking mount and making sure that the LCD is flipped out away from the camera body, but if you want any terrestrial foreground, you're stuck with higher ISO and noise.
The 60Da is an option, but only if astrophotography is a big enough part of what you do to warrant having a filter, with all of the drawbacks of having an extra optical element, on your camera for most of the rest of your shooting.