Which full HD monitor, LCD or LED?

1st off don't confuse bigger with better. At the same resolution, and all other things being equal, the smaller monitor will have the sharper picture.

The 23" has a dot pitch of 95.78 whereas the 21.5" has a dot pitch of 102.46 This means that the smaller monitor has 6 more pixels per inch of screen real estate. For many peeps, at the standard PC viewing distance, 96 is the minimum pitch below which the image will appear "grainy". I don't think you will notice any "grainyness" on either but all things being equal again, the 21.5" will appear sharper.

LED's, in general, are brighter, thinner, lighter, consume less energy, produce more accurate color, are more reliable and last longer.