I actually have a Eee PC 901 (Intel Atom 1.6 GHz, 1 GB RAM, 12 GB total storage, Windows XP) and have been using it for light programming using Eclipse for the past three months. At least for my uses, the Eee PC 901 has been more than adequate and I've been happy with it.
Keyboard
The keyboard may be a little bit on the small side, but after I used it for a few days, I got used to it and haven't had a problem with it. In fact, I've connected a full-size keyboard to it for the past week or two, but I still prefer the small keyboard because I don't have to move my hand around as much.
Performance
In terms of performance, the processor may be a little bit on the weak side, but the bigger problem I've had with the Eee PC 901 is that the solid state drive can slow down quite a bit when there's lots of disk IO. However, you mention the Eee PC 1000H which has a hard drive, you may not have the problems that I am experiencing. But other than that, I've found the Eee PC to be quite a snappy little machine.
Screen
The screen may be one downside indeed. The vertical resolution is on the low side (only 600 pixels), so you may need to configure your IDE to reduce the number of tool bars that are displayed on the screen. Also, you may want to change the Windows theme to Classic, as it will save you a few pixels here and there.
The 1000H model has a 10" screen which may be easier on the eyes than the 8.9" on my 901, but as with the keyboard, I've come to be accustomed to looking at the small screen. Also, one upside to the small screen is that the display is very sharp and crisp.
Battery Life
Battery life on the 901 is pretty good. In fact, I can get about 5-7 hours per charge, but do keep in mind that the 901 has a 6-cell battery and lacks a hard drive, so it may have a longer battery life than the 1000H.
Size and Weight
In terms of size, the 1000H does seem a little bit bigger than the 900 and 700 series, but that's something of a preference and you'll probably want to look at the actual units to see the difference. I believe there is also a weight difference of about half a pound between the 900 series and 1000 series.
Comparison of Models
If you want to see a comparison of the different Eee PC models, the Asus website provides a comparison list of Eee PC models.
Conclusion
On the whole, I have been enjoying my Eee PC, and I think it would be perfect for taking around and programming on the go. It may not be suited for heavy development, but it sure is enough to use Eclipse with my Java and C projects.
Oh, did I mention that I am posting this answer from my Eee PC?