Never had a problem with my 400D, does great for Astropics as well as normal photography, turn the Display off during the night as its like using any other DSLR, only issue I have is the bright green light on top which can be fixed with the right modeling paint

I have only ever once ran out batteries and that was before I bought a new one. If that concerns you, buy an AC adapter. As for dust removal, I have seen dust bunnies disappear from my images a couple of times now after a quick power down and power up. The 350D and 400D are great cameras for Astrophotography, whichever one you decide on will give you loads of fun.
BTW once you start in Astrophotography it will send you broke

You will always want something more, I know, I am still sending myself broke LOL....
Good luck with your decision.