Umm... the VIA C7 processor on the HP 2133 is seriously under-powered compared to the Celeron M 900MHz on the Eee. I can say that Celeron M 353 is at least on par with VIA C7 at 1.6GHz (and at most faster than VIA C7 1.6GHz in anything), which just means that the highest spec'ed HP 2133 is still a bit inferior to Eee PC. The bigger screen and bigger hard drive are a plus though, and ample RAM right from the get-go is also a big plus. Just don't expect any miracle with the specs that you have on the HP 2133.
By the way, as for how Eee looks in the sun, thanks to the anti-glare filter, you can see the screen really clear even outside, on a sunny day. That was with 25% brightness. The only downside is that the anti-glare filter dims the screen about 5-10%, but that's a good price to pay, considering now you only need 20-25% of the brightness out in direct sunlight. (no pics will be able to show you this. The glare of the sun will affect the lens and kill the picture, or at least that's how it is for my camera...)
Another thing that might interest you: the Eee PC has an IGP that supports Pixel Shader 2.0, although there is no Vertex Shader. Lighting and Transform is done by software, which may kill performance in some games, but not so drastically. In the end, you have the ultimate 1998 - 2003 gaming machine that is quite portable, and will work for quite a while before its battery runs out.
There is also an option to solder a Pentium M ULV 1.20GHz processor in, which will increase performance to an even higher level while not sacrificing much of battery life, if at all.