This question is pretty common these days and doesn't really have a cut-and-dry answer. I personally own a white Macbook and an HP Mini 1030nr (netbook), but no Air - I love both of my machines, but for completely different reasons. The Macbook does everything I throw at it well (well, almost everything) - the HP Mini is much slower, but it handles basic tasks well. I take my HP Mini almost everywhere now - it is so small and light that it almost never gets in the way. Also, at just $399 (same ballpark price as the EEE 1000HE) I don't worry as much if something happens to it (not that I want anything to happen to it).
Here's my take - if you really want a Mac, a netbook is a no go, unless you want a hackintosh, and that's a bit of work. However, you have a nice iMac already, so do you really NEED another powerful machine? I would say no, but I don't know your situation. I personally do not NEED my Macbook, as I have a Mini that is A-OK with me, but my WIFE needs the Macbook, so I digress... If you NEED another powerful machine, get the Macbook (I don't recommend the Air due to its "restrictions," even though it is dead-sexy - and the Macbook is less than 5lbs itself now). If you don't, get the netbook - it'll save you money, weight, size, and worry, all while providing a good computing experience (at a ~2001 speed
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P.S. - Look at the HP Mini 1000 series. I can't speak for the EEE 1000HE since its new and haven't actually seen it (I assume you haven't either), but the HP Mini is a WAY BETTER machine than the EEE 1000H - I was originally tossed up between the two until I compared them side by side. The HP is much more solid, has a better keyboard, and just looks great (not a Mac, mind you, but not that far off). It was better to the point that I paid $70 more for the HP than the EEE 1000H, mostly just for build quality and looks. Good luck.