The short answer: No, they won't look "sharper".
The 23" display has got more pixels, but it also has a larger area to display these pixels. So every single pixel will still be about the same size (about 0,25 mm or 1/100 of an inch). The size of a single pixel is obviously what determines how 'sharp' something looks. The smaller the pixel, the sharper the image. Simply having more pixels doesn't mean that much for sharpness: imagine having those 1920 horizontal pixels of your 23" screen but now they're spread out over a screen that's about 15 meters in diameter (and you sitting close to it) Obviously this wouldn't look 'sharp' since every pixel would appear about 8 mm in diameter now.
You can't (yet) make pixels infinately small, for simple physical reasons, but there are examples of much sharper (higher dpi-value) displays than our computer screens: printed text. A typical printer will print black text with a resolution of 600 or 1200 dpi and a professional press will even get higher. That's why a page in a magazine looks that much sharper than your typical screen.
edit: I'm definitely too slow