DisplaysShouldNotBeTVs
Update:
Sorry, the 3DS comparison was backwards, I just tried both my original 3DS and new 3DS again yesterday and the original (2011) is much better.
The 2014 new 3DS top screen feels washed out and the brightness level always feels too low or too high. On the other hand, despite some extra glare, the contrast ratio on the 2011 3DS top screen is "just right" — bright but not harsh — it feels less blurry and it's much easier to tell what's happening in the game. The horizontal lines are also less visible on the 2011.
The 2014 technically has more comfortable stereoscopic 3D, but the 2011 wins by a large margin when just used as a plain 2D screen.
Trying a 2DS is also a good idea since it doesn't have the horizontal lines, but I've never tried one myself so I can't directly reccomend it.
(Side note: the bottom screen is actually great on both models, but that's less important because the top screen is where you're playing the game.)
Outside of the 3DS series, the original DS and DS lite are still the most uniquely comfortable devices I've ever used due to their extremely crisp pixels + lo-fi graphics with essentially zero post-processing.
BTW, if you are intending to play both original DS and 3DS games: the backwards compatibility feature on the 3DS looks terrible, since the resolutions don't match up. You only get the choice between extremely blurry scaling or squinting at a tiny box.
I personally don't use the 3DS backwards compatibility at all and heavily reccomend just buying both generations of systems.
TLDR
Original systems:
2004 and 2006 are perfect. Zero strain.
If you had to stop playing games due to strain, these systems might be a breath of fresh air!!
Get the 2004 if you want a transflective LCD and the option to disable the backlight entirely when outdoors.
2008 DSi screen feels harsh — don't buy that one.
3DS systems:
2011 is very good. Looks sharp enough and totally playable for me with minimal strain.
2014 (small version): not terrible, but feels washed out, too low contrast, and something feels off about the backlight. Sometimes causes dry eyes afterwards.
Playing original DS games on a 3DS is uncomfortable, in that case just buy an original system instead.