My list:

#1 Ace Attorney Investigations: Miles Edgeworth

#2 Metal Gear Solid: Peace Walker
Surprised Peace Walker didn't make the list. Sure it was on handheld but it was such an amazing game with interesting mechanics.

#3 Lost Planet 2
This game was so much fun but there was a level pretty early on that required a good team play which I sometimes failed because someone got kicked out and made it frustrating to get through. It had some serious hidden stuff that really elevated the game if you knew how to do it. Also taught my cousin a skill that got him a world record at the time on one of time attack stages but has probably been beaten since you can cheat on it somehow.
This is probably one of my favorite co-op game simply because there is not many like it.

#4 Vanquish

HMs:
Gran Turismo 5
Didn't play enough of it but I always loved GT games

Valkyria Chronicles II
Co-op lets you basically have an extra character so it was pretty easy but soloing was fine too. I loved the classes that split to pick which speciality to go for so it was really fun. Escort missions were the big minus but I didn't mind the cliché high school setting outside of awful laugh from protagonist Avan.

Yakuza 3

Mafia II
This was a really good game and I like some music from that era. Big fan of Dean Martin. Sadly lack of side stuff and freedom puts it behind other stuff

@tokyoslim I played Yakuza 3 on HD collection. While I loved Revelations and some story moments, the gameplay was clunky and easily the worst with enemies blocking too much. It was a PS3 game that still felt like a PS2 game. I did like guns doing more damage than other 2 on the collection which were bad.

Vanquish is amazing game. Only dowsides are its lenght=enemy/environment variations=it wasn't enough.
Also you had to pay if you wanted that special weapons or something. Tri-weapon pack. Think it was a pre-order bonus and later could be bought

The Last of Us 2

I didn't like the 1st one so recapped it before playing this. I still hate encountering enemies in these. As much as I agree that there are too many resources, the game forcefully limits your inventory which I hate even more considering there is possibility to have so many fights and end up fighting a boss without really anything. Gameplay has improved quite a bit but I felt I played this like an MGS game instead of like a ND game.

The game is long but it had evenly good moments I liked and has lots of Uncharted 4 in it. ND is amazing giving you beautiful game with animations and subtle things. It is technically an impressive game and wanted to give them another chance but I just don't like this type of game that annoys more than pleases.
I didn't mind too much on a story but I didn't hate it nor love it. It is what it is. And I did tear up couple of times.

Final Score: 7.5
-American Football Roller Coaster-

Sad but I expected Ace Attourney: Investigations to rank low if at all since it was already late in DS life cycle and didn't sell well. I love it because it is so different from main games and has Edgeworth as protagonist along with good old Gumshoe and "a thief". Also it being more detective/puzzle is a bonus.

I watched 5 minutes of Scott Pilgrim vs the World movie and it felt like a waste of time which I have never done to any other movie. The game is good but never finished it because my friends levels always reset and it was bothersome to even go through things again so there's that

90% gameplay
10% story

A good gameplay makes me stick with a game easier than the story which I can just watch on YT. Of course I'm more invested if I had played it myself.
And it varies by genre too since some "gameplays" are just reading and picking choices while others is just all about timing like rythm games that has more to do with music so sound based "gameplay".

Like I didn't like The Last of Us for the most part since gameplay is lesser than Uncharted that has doable gameplay but at least has that verticality among others and really hated the crafting in that game.
Sekiro was just monotonous with finishers and mikiri counter was just too easy to pull of that it was getting repetitive which is why I didn't like it either.

And yet I like games that have lesser gameplay than either of them. So it comes down to the tools the game provides and whether I like to use them in the game itself is the gameplay judgment.
Storywise I appreciate if it has smart writing but I also like campy/cheesy stuff. Even bad dialogue doesn't bother me much so a good story is just a bonus for me most of the time.
Probably why I go toward more japanese games than western games. Japan for long time and still majority has mentality to have games more focused on fun factor while western is more on immersion. Of course nowadays there are less focus from some people and indie games are good at giving you more variations.

I mostly play games I'm interested in or at least had a decent impression that I want to try them so I skip plenty of stuff because life is short and have no time to play all of them while also having a huge backlog.

I was awed when I learned the paths were connected to each other in the World. It is simply amazing from level design point. I co-oped with my cousin a lot in Demon's but sadly this game went backwards in this. Why it's only 3rd on my list is simple. About half of the bosses sucked as they were just boring. Also Blight town and the swamp area. Yikes that framerate.
Best fight is easily in DLC. My cousin saw me beating him and it was glorious.

Uncharted 3 has some amazing set pieces but it also has couple of things I don't like making it my least liked in franchise. If you have played CoD: Black Ops you will know what I hate and is my most hated thing in a game. It feels cheap and is a huge annoyance.

I enjoyed puzzles in Catherine. Challenging but never thought they were that hard. I had way more trouble choosing answers to get the ending I wanted. Versus mode was pretty good since it can get really tricky when you try to sabotage each other.

First time I saw a trailer for Ghost Trick, I was already in. I had just finished Ace Attourney Investigations and was craving for more stuff from them. This game is so different from them yet familiar. This game is god vibes and it's better to experience it 1st hand so I won't spoil it.

Yakuza 4. Kinda reminds me of TMNT. It's great and my 3rd favorite in the franchise. Bold move to go with 4 characters but it worked out pretty well in the end. And some really top moments of the series.