Considering its handheld origins, Liberty City Stories is a tremendous achievement and a must have for GTA fans.
Liberty City Stories tells the tale of Toni Cipriani, who most fans will remember from his appearance in GTA III. Toni is a no nonsense guy who works for the Italian mafia and is very close to their boss, Salvatore Leone. He also has a strange relationship with his mother, whom no matter how hard he tries to please, never views him as a worthy son. Unlike in other GTA games where something memorable takes place at the start, LCS starts with Toni arriving on Liberty City... and not much else. Toni then meets up with Salvatore who tells him to warm up to some of the lower mafia bosses. This doesn't please Toni too much, but he follows suit. From here on Toni gains employment with several of the big personalities in Liberty City (including some of the characters from GTA III) and performs most of the jobs you'd expect from a GTA game. Toni's biggest tasks involve helping Salvatore fend off the local gangs that want to take away power from him and assisting local media mogul Donald Love in his quest to become the major of Liberty City.
Frankly, the story in LCS is much less memorable than that of other GTA games. You never quite get the same epic feeling of previous games and much of the characters aren't all that memorable. Toni's motivation is basically money and whatever his current boss wants, so it's a little harder to sympathize with him in the same way it was to Tommy Vercetti or Carl Johnson. There are very little plot twists and none of them have a really major impact on the story. Even the ending feels pretty hollow since the major antagonist in the game is someone that barely features in the story.
So compared to the previous games the story feels a bit light and not quite up to the series standards. That's not to say the story is bad (it sure isn't) or that nothing memorable happens. There are lots of great cutscenes and some hilarious interaction between the characters (the cutscenes involving Maria and Salvatore are pure gold). Most of the good stuff comes from bits that fill in some of the blanks from GTA III. The dialogue itself is pretty sharp and there's plenty of humor involved. As long as you forget about the epic scope of previous stories in GTA games, you'll be able to appreciate the story in LCS.
As for what can you expect from Liberty City Stories' gameplay? Pretty much the same stuff from previous games. Basically you have the core gameplay of GTA III with some of the enhancements of Vice City. Most of the missions in LCS are your standard crime jobs except that now some of them are extremely short. This is one of the main complaints against the game. Very few (if any) missions get into epic territory, with some of them being extremely basic, even as you reach the latter stages of the game.
There sure are plenty of good missions though, such as one where Toni has to take out three celebrities arriving on Liberty City at different spots. Another mission pits you against twelve chainsaw wielding maniacs in a locked room (one of the most challenging and potentially frustrating missions of the game). The missions involving Donald Love's campaign feature plenty of great stuff as well as many references to GTA III and Vice City. The same goes for Salvatore's line of missions which culminate in an exciting shower of bullets across the sea. Overall the mission design is good but once again, not up to the series standards.
The side missions in LCS are pretty similar to previous games. There are the standard vehicle missions (Taxi, Vigilante, Firetruck, etc.), hidden package collecting, rampages, unique jump stunts, and car collecting missions. There are also some interesting side activities such as working as a car and bike salesman or joining the local Avenging Angels gang (a gang intent on stopping crime in the city). LCS features several hours of fun through the side missions which combined with the main story missions as well random wandering across the city makes LCS a pretty lengthy game (I spent close to 50 hours on the game without ever really wasting time).
One thing LCS does very well is set the contemporary tone for 1998. Late 90's culture is mocked to the fullest here, particularly on the radio. The rise of the Internet is the inspiration for dozens of jokes revolving around a group called Citizens United Negating Technology For Life And People's Safety (C.U.N.T.F.L.A.P.S.). Several commercials play on all the radio stations mocking ordinary (and not so ordinary) situations and blaming them on the Internet. The talk radio stations are absolutely hilarious too, mocking the rise of technology, ecologists, religion, and pretty much everything in between. The DJs in each radio are also great, some of them making a return from GTA III. There are also plenty of dark references to GTA III, which will be much appreciated by those who spent hours listening to the radio in GTA III.
Of course that the radio is not all talk shows and jokes. There's plenty of great music in LCS, some of it licensed and some of it custom made for the game. The custom music is actually phenomenal and you'll likely be very surprised to find out which songs in particular were custom made for the game. What impressed me the most about the song selection in LCS is how it fits the time period perfectly and how each radio sounds in accordance to the type of music they played in GTA III. The only problem with the soundtrack in LCS is that it's really short. Presumably this was due to its origins as a handheld game and the PSP's limited storage.
Visually, LCS is almost identical to GTA III and Vice City. The game actually uses a different graphics engine but the end result is very similar. Prior to Grand Theft Auto IV none of the GTA games were known for hot graphics and that's the case here. There's plenty of detail in the city but textures are a bit bland and character models are blocky. Again, due to its original handheld nature this is pretty forgivable. Besides, like with previous games the art direction behind the graphics is phenomenal so even with limited technology the game still looks great.
As for any differences between the PS2 and PSP versions, there are none as far as game content is concerned. The only difference is that the PS2 version lacks the multiplayer modes of the PSP version. Honestly, that's hardly a loss since the multiplayer from the PSP version wasn't exactly mind blowing, so that really shouldn't be a factor to consider between both versions.
Judged on its own merits and trying not to compare it directly to the major GTA games, Liberty City Stories is a truly great game. Its got everything that makes a GTA game fun and features many details that fans of the series will greatly appreciate. Set your expectations accordingly and enjoy this great trip back to the city that kick started the revolution.