When reviewing GTA3:DE, there are two completely separate yet equally important elements to discuss: the design of the game itself (which is more or less unchanged since the original PS2 release in 2001) and the remaster.
As a remaster, the "Definitive Edition" disappoints on almost every front. While the original was built on the RenderWare engine, Grove Street has essentially recreated GTA3 in the Unreal 4 engine. The result offers clearly superior graphical fidelity, while making a number of minor, unnecessary changes, and adding a number of bugs. The sole positive design change is the option to reattempt a failed mission directly, although the lack of mission checkpoints (as introduced in San Andreas and used in every subsequent game) is a missed opportunity.
Thanks to Unreal 4, the Definitive Edition supports modern widescreen resolutions, adds dynamic light sources and shadows, and adds a suite of standard post-processing effects (like Anti Aliasing and Screen Space Ambient Occlusion). Many (though not all) textures have been replaced with higher resolution versions, and cars have been updated with higher polygon-count models. The performance is nothing short of atrocious. Even on top end hardware, the game stutters and the frame rate dips. For a 22 year old product, this is simply unacceptable. The changes also amount to a downgrade in the graphical style of the game. Gone is the moody, foggy lighting of the original. New textures often clash with the style of the older ones, and AI upscaling has been used with unimpressive results. Its almost an achievement that the "Definitive Edition" of the game looks worse overall than the original PS2 release from 2001.
As far as the game itself goes... it's a mixed bag. This really is the game that started it all, and it can be difficult to judge by modern standards. Not only is it the first game published under the "Rockstar Games" name, it's the first game to bear the "Rockstar North" logo following the acquisition of DMA Design. While the overall layout of the game owes most of its design to the original Grand Theft Auto from 1997, the jump to 3D had a tremendous impact of the overall game experience. And while it is hardly the first open world game, it is the biggest and most memorable example of the early genre.
GTA3 follows the standard GTA formula established with the original game and that continues to this day: you play as a criminal in a large, open city. As in GTA4, the Liberty City of GTA3 is divided into three sections, with the second and third unlocking as you complete key missions. You can steal any car you see, and generally cause mayhem for fun. Missions are sprinkled throughout the world, taking you out of the "free-play" experience and giving you specific tasks and limitations. You can take available missions in any order, although certain mission givers are gated behind the completion of specific other missions. The result is a more or less linear path through the game. Missions generally involve killing or destroying specific targets, racing to preset objectives, or escorting NPCs around the map (or some combination of these). They range wildly in difficulty from foolproof to extremely challenging, and while many are fun, some can be quite tedious or frustrating.
Together, the missions compose a very simple story. The protagonist is betrayed by his girlfriend in the opening cutscene, then works for a serious of gangs before ultimately confronting her. There's not much to it, and while several recognizable actors voice some of the NPCs, the story is ultimately one of the weakest elements of the game.
In addition to story missions, there are various other tasks that can be completed, such as picking up fares as a taxi driver, rescuing injured people in an ambulance, putting out vehicle fires in a fire truck, killing criminals in a police car, or delivering specific vehicles to a lockup. There are also a large number of hidden packages to find, a number of "rampage missions" which involve killing a number of enemies with a particular weapon within a time limit, and 20 stunt jumps to complete. These are of extremely limited entertainment value, but some of the nicest rewards in the game are gated behind these tasks and they are required for 100% completion and the associated achievements.
Unchanged from the original is the frustrating driver AI, wonky car physics (many vehicles seem to have a center of mass above their roof), and irritating design choices. As you progress through the story, various gangs become hostile to you, with endlessly respawning, heavily armed gang members essentially making it impossible to traverse certain areas of the city. Several of the stunt jumps require landing in a very precise spot to register and can take dozens of attempts to complete. Police can arrest you simply by being near the vehicle - more than once I had them essentially warp to the car, and once they touch the door handle they will almost always succeed in pulling you out (I even had one arrest me mid-air while my vehicle was upside down and tumbling). It rarely feels like an earned fail state. Vehicles are extremely vulnerable to weapon damage, and will catch on fire and detonate very swiftly when shot.
Overall, GTA3:DE is a subpar port of a groundbreaking game that aged very, very poorly. Having finally completed the 100% achievement, I can confidently say I never want to play this game again. Unless you are the most determined completionist or dying of nostalgia, I would avoid this title.