The main difference between T410 and T420 screens is the overall pixel ratio. The T410 offered screens of 1280x800 (WXGA) or 1440x900 (WXGA+). Both are 16:10 ratio and were rated at 220 nits and 300:1 contrast. The T420 came with 1366x768 (HD; 200 nits) or 1600x900 (HD+; 250 nits); those are 16:9 ratio and 300:1 contrast ratio. As I only have the T410 WXGA+ and T420 HD+ screens, all I can say is that they both have fairly poor off-axis viewing angles. I haven't noticed any brightness difference between them (the T420 is supposed to be brighter). Although I generally dislike widescreen displays on laptops, these aren't too bad.
So I guess it really depends upon what T410 screen you have now, and what you can find in a T420. Assuming you have the WXGA, I think a T420 with the HD+ screen would be a step up.
No personal experience with the T5xx series, sorry.
Click on thumbnails below for full-sized images (2048x1536 ~500KB each; T410 WXGA+ is on left, T420 HD+ on right):
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#1 is Windows 7 desktop. You should notice right away that the T420 has a "shorter" screen.
#2 is Firefox browser. Both of these screens have 900 vertical pixels but the T420 is shorter than the T410. This means that the type and icons on the T420 will be a little bit smaller than the T410.
#3 is a closeup of the Firefox browser.
#4 is an offaxis view from above the screens. The T420 screen may be washed out compared to the T410 due to it being slightly brighter.
#5 is a similar view to #4 but I've adjusted the camera's exposure. Both screens were set at maximum brightness. The difference here I believe is due to the smaller aperture ("f-stop") I set on the camera.
Note that the brightness of the screens will not be uniform across the range of laptops. Variations due to age or factory processing will occur.