If, for LED, you mean "LED backlight", it is the consensus that they are to be preferred to CCFL illuminated screens.
If you mean "OLed" - I don't know of any such build.
check things using the http://forum.bongofish.co.uk/index.php?topic=1984.0
Options for a 23" - None that covers the whole screen
Options for a 22" - (22" are 16:10, 21.5" are 16:9)
That cover the whole screen, the cheapest would be the Intuos 3 12x19.
It also has hotkeys, which make dismantling the Wacom and assembling the DiY a bit more challenging, but allow some very interesting option like having a "swap screen" button, that is useful on multi-monitors set-ups.
Also, there is no problem with drivers availability.
Cons: they cost easily twice or more the next alternative, or a 1/3rd of an Intuos 4 Extra Large (12x19.2).
If you can accept to have a couple of cm that are left out of the active area, where you have to reach with a mouse or something
, you can use Intuos 2 (series XD) or Intuos 1 (series GD) 12 x18" . To remain inside the active areas, these accept at maximum a 21" 16:10 or 4:3 monitor. Alternatively, LG is selling the LG 20MP48, that is a 19,5", 16:10 (1440x900) LED IPS screen that could be a nice prospect - I am going to try my hand with this combination, Intuos 2 + LG, some time soon (next week or so)- You may hold on for a while, and see if I post news on it
However, while the drivers for these older tablet may be installed in newer OSes like Windows 10, it may require a bit of wizardry (I stick with Intuos 2 and Windows 7)
If you are an open source enthusiast, in Linux the driver issue and the availability of hotkeys do not matter, as the Linux wacom project driver handles virtually everything Wacom has ever produced, and scripting allows to implement the swap screen buttons - and similar features - quite easily.
16" - there are really no options for that specific size.
15.4" (16:10) Intuos 4 L (PTK 840) - it may cost as a big Intuos 3, though, and it is not such a great improvement over the Intuos 3
- it is smaller than the panel by some 17-20 pixels that, well spaced, becomes a negligible 8 pixels-wide border.
15.6" (16:9) - The same Intuos 4L , but the "unreachable" part of the screen becomes much more noticeable, especially on the vertical border(s).
15" 4:3 -> Every 9x12 and 12x12 tablet (Intuos "Large" up to the 3 series) fits perfectly ( a bit too much... requires a precise assembly).
As a side note, in Windows a program called "Power strip" allows to restrict the output of the computer so that it matches an arbitrary resolution inside that of your screen, effectively "cutting" out unwanted (unreachable) parts of the monitor.
I never used it, but it is a possibility.