Technically this would be the third time I'm playing this, since I've played the original on genesis as a kid and the psp version of this one, so I should assume I know what I'm talking about.
Anyway lets get started.
This is widely considered to be the best Ys game out there by many. In my opinion that can be debated (Ys IV - Dawn of Ys on PC-Engine remains the best one for me), but this is an amazing game nonetheless.
Essentially it's a total remake of Ys III. It ditches the side scrolling nature of the original and replaces it with the gameplay and engine of Ys VI on PS2, though vastly improved.
Story wise it's the same as Ys III: It takes place after Ys IV, Adol and Dogi visit Dogi's homeland,♥♥♥♥ goes down etc. etc. Don't expect anything groundbreaking. That's not what Ys is about. They have however fleshed out the characters a lot more this time around and Adol is once more a silent protagonist (like he should be).
Gameplay wise is where the game truly shines. Similar to the older games you move in a 3d environment. However unlike I, II and IV now you can jump, do various attacks and cast spells once you get certain items. Technically Ys III already had that, but this particular style of gameplay started with Ys V. Combat is fast paced and extremely satisfying, enemies drop gold and items that give you temporary bonuses when you pick them up. You can upgrade your equipment using a specific ore, but despite what an NPC tells you, you won't be finding it anywhere but in chests up until late in the game, so you are encourged to explore everywhere, there are plenty of goodies for you to find. Boss battles are hard, but not frustrating like some people will tell you (you can't #YOLOSWAG it through the game unless you're playing on the lowest difficulty in which case go jump infront of a train, you filthy sсrub).
Graphics wise it uses the same engine as The Ark of Napishtim, though characters are once again sprites instead of 3d models.
Regardless it looks and runs great even on a toaster so you won't have any issues running it.
Ys III, despite being an oddball game had some amazing music, arguably some of the best in the series. They completely re-arranged the soundtrack here using real instruments and trust me on this one: the result is mindblowing.
Some might ask what the difference between the PSP and PC versions of the game is.
Well like I said before: The PC version looks and runs great at constant 60fps even on a toaster. The PSP is locked at 30 and obviously has a lower resolution (though the camera has been zoomed out to compensate for it). The PSP version however has a slightly better translation, voice acting (which varies from decent to terrible), a double burst ability which makes Adol even more powerful and allows him to regenerate health when attacking enemies, and the option to choose between 3 different soundtracks (regular, PC-88 or the X68000 version), it however lacks the PC-Engine music which is a damn shame since it's amazing.
Overall I'd stick to PC, though if you've got to have the game on the go have at it.
All in all its an amazing game, with a fun story, great gameplay, pretty visuals and amazing music.
I recommend it to any Ys fan or anyone who likes proper action-RPGs.