I have been realizing that it's not always obvious by genre which games I want to play on handheld, and which I want to play on a big screen tv.
Sometimes a game is suited to both...but a few retro games have sucked me in where others do not and the list does not necessarily make sense to me.
After a month of trying out many games both retro and recent(ish) I have gravitated to a few.
On the retro, the PC engine version of military madness is really fun on a handheld even with the tiny screen. I prefer this version over the PS1 update and it is great! presumably because the turn based mechanics and easy controls. Also as a C64 kid I liked OG pirates and pirates gold, and the genesis version, which I had not previously tried has been a lot of fun.
I have also liked, Tetris, columns, , angry birds, most shooters, crimson land, Age of Zombies, the "stealth" games ie "stealth 2, a game of clones", super meat boy, Worms, puddle, and I am sure to find more.
Games I thought I would want to play but did not enjoy on a handheld: sonic, god of war, bullet hell shooters, racing games, Papers please, RPG's Borderlands 2 and pretty much anything with text, not turn based or level based action. Sometimes it was the small screen and others it was just not fun.
On the big screen, I also really enjoy Crimson Land, and the "Stealth" platform games, as well as a few shooters that allow you to level up as you play.
I think the nuances of the small screen and my short attention span are the foundation. But some games seem to break this trend? The introduction to save states is also a factor. Games where I would have had to start over in the old days are more accessible now.
In the end it comes down to preference. I have not had modern AAA rpg and adventure games appeal to me in ages. Despite wanting to play those longer games. Even good games like hollow Knight are not my bread and butter. so YMMV.
But my point is, that many of the older games translate very well to the small screen and are more suited to handheld play while some play better on a TV.
What games do you want/like to play on a handheld?