I know the EOS has a bigger sensor and more megapixels (12 vs 15)
This really isn't an issue. This works out as a mere 11 percent different between the linear pixel counts (i.e. it's 25% extra over the area, but only 11% extra on the side or height). You won't notice that in practice.
but the FZ200 has a constant F2.8 aperture through the entire 25-600mm focal length. The best lens I can afford to get for the EOS is the kit EF-S 18-55mm f3.5-5.6 IS II.
These are two quite different cameras. The FZ200 is really intended for travel and convenience photography. It's a relatively small package with a versatile lens. The compromise you make for that is the small sensor.
The 500D is a DSLR with a large sensor.
Ultimately the 500D would be my choice for astrography, but then I'm not the one doing this. :-) The larger sensor simply wipes the floor with the small FZ200 sensor for this purpose. And you also get the benefit of better control of depth of field with a large sensor (which in layman terms means it's easier to get those out of focus backgrounds).
But the DSLR cannot easily (or cheaply) get you a huge zoom range. And I suspect you may be planning to use it without a telescope for astrography. Most people doing this seriously would be bolting a DSLR onto a real telescope.
I do not think you could use an FZ200 with a telescope (someone please correct me on this if they know it's wrong).
Well you can add something like a used/old 18-200mm to your DSLR. That's equivalent to about 28-300mm in the same terms the FZ200 uses.
300mm sounds a long way from 600mm doesn't it ?
But it's not as bad as you think. In practice you can crop most of the way down, and I'd honestly prefer that to the FZ200 for "everyday" purposes, but for astrography it's a different issue.
I also know that the FZ has a very fast focus (my current S2980 takes an age to focus and my wife hates it lol).
I would not expect too much from it. Amateurs generally have an expectation of fast focus that exceeds what is practical in most cases.
I've seen some of the astro shots taken with the FZ online and they are very impressive so I know it can handle those types of shots.
I have seen some interesting shots which were stated to use "only" the FZ200, but when I got into the detail it appears they often used star trackers, which are somewhat expensive bits of equipment to avoid star trails (and generally something serious astrography types will use).
SO I'd be careful about your expectations of what is possible.
Astrography really needs a telescope and quite a bit of technique (often in post processing as well as when you're shooting). Dpreview.com have a forum on this very subject and I'd strongly suggest reading posts there and perhaps asking them some questions.