Both netbooks are well designed, featuring a comparably beautiful finish that is bad for fingerprints but nice if you keep it clean. As long as you get the newer models, both sport comparable screens as well (Asus previously had a lower quality screen but recently brought theirs up to speed). The main form differences come in the layout of the keypad and keyboard. This simply depends on what you like.
Asus: Has a flattened keyboard which allows for wider keys but less key differentiation (they are not pyramid shaped like normal keys are). Some of their models feature a touchpad that is built into the form and designated by a textured surface rather than a pad (see pictures). This is an excellent innovation that makes using the touchpad much easier. Also, all of the Eee PCs I have seen sport a screen that, when open, dips down slightly behind the keyboard, which is a little different than the way normal laptops are built.
Acer: The main thing to get used to here is the way Acer has toyed with the keyboard and touchpad setup. In many models they placed the right and left click buttons on either side of a rather small touchpad which can lead to difficulties in navigation, although with many new models they have gone back to a traditional touchpad. Still, the largest complaints people have about the Acer is the small touchpad and cramped keyboard. As a plus, an interesting innovation was to place the page up and page down buttons above the right and left buttons, which allows for much easier navigation through websites, word files, and pdfs. In a lot of their models the screen, when open, sits above the computer slightly which I prefer to the sinking of the Asus
Another note on form: If you get the 6 cell battery it is a little larger than the 3 cell and will protrude slightly, especially in the Acer. However, while it look a bit odd from the side, it is designed so that it sits well on a desk or your lap so it is no problem.