I guess whether it's squished depends on how that monitor handles 4:3 resolutions.
Any convertor box that converts composite, RGB or S-video into VGA is going to produce a pretty ropey picture (with the upside that it's easy to get working).
The xbox actually provides both component and VGA outputs from its AV connector, although these are only available if you have a modchip or an NTSC model. I've used both outputs and they are pretty good. Very few monitors have component inputs, but for VGA, you might want to try this:
http://www.x2vga.com/
As I'm a cheap-skate, I made a VGA box myself from a schematic I found on the web (uses a chip to extract the sync signal) that provides a nice 640x480 picture into my monitor. Sadly it only support sync-on-green monitors though