The remake of the original Mass Effect is not a from-scratch rebuild, but will be a "modernized" experience, allowing players to experience the original in the "best possible form" - so I imagine, as with BioShock, there'll be some updates, compatibility fixes, and generally enhanced textures and graphical effects, all baked onto the original engine. It also aims to bring the original trilogy together in one, seamless experience.

It seems it won't be entirely as it was, though - with BioWare detailing a number of planned changes to the trilogy today that players can look forward to. It includes some we knew already, such as the Mako getting better handling, but there are some other changes to gameplay too. 

Combat is also getting some changes, which makes sense, given the original Mass Effect actually played rather differently to the second and third games. According to BioWare, they have turned the game's mechanics to give it better handling without "scrapping the spirit" of the original games, in order to make the experience consistent. 

There's a huge list of gameplay changes, which are all rather subtle but combine to make a big difference, the full list is below;

• Shepard can now sprint out of combat
• Melee attacks are now mapped to a button press rather than automatically occurring based on proximity to an enemy
• Weapon accuracy and handling has been significantly improved:
• - Reticle bloom is more controlled
• - Weapon sway removed from sniper rifles
• - Aiming down sights/”tight aim” camera view has been improved
• - Improved aim assist for target acquisition
• All relevant enemies now take headshot damage in the first game (Previously some did not, including humanoid enemies)
• Ammo mods (Anti-Organic, Anti-Synthetic, etc.) can now drop throughout the whole game
• - Previously, these stopped dropping at higher player levels
• - They are now also available to purchase from merchants
• All weapons can be used by any class without penalty
• - Specializations (the ability to train/upgrade certain weapons) are still class-specific
• Weapons cool down much faster
• Medi-gel usage has been improved
• - Base cooldown reduced
• - Levelling benefits increased
• - Increased Liara’s bonus to cooldowns
• Inventory management improvements
• - Items can now be flagged as “Junk”
• - All Junk items can be converted into Omni-gel or sold to merchants at once
• - Inventory and stores now have sorting functionality
• Some abilities have been rebalanced
• Weapon powers (i.e., those that are unlocked on each weapon type’s skill tree) have been improved:
• - Effectiveness/strength is increased (duration reduced in some cases)
• - Heat now resets on power activation
• Squadmates can now be commanded independently of each other in the first Mass Effect, the same way you can command them individually in Mass Effect 2 and 3
• Some boss fights and enemies in the first game have been tweaked to be fairer for players but still challenging
• Cover has been improved across the trilogy
• - Additional cover added to some encounters
• - Entering and exiting cover is now more reliable
• XP has been rebalanced in the first game 
• Ammo drops have been rebalanced in Mass Effect 2 

There's also a ton of new enhancements across the entire experience, which include;

• New unified launcher for all three games
• - Includes trilogy-wide settings for subtitles and languages
• - Saves are still unique to each game and can be managed independently of each other
• Updated character creator options, as mentioned above
• - FemShep from Mass Effect 3 is the new default female option in all three games (the original FemShep design is still available as a preset option)
• Trophies across the trilogy have been updated
• - New trophies have been added to the trilogy
• - Progress for some now carries over across all three games (e.g. Kill 250 enemies across all games)
• - Trophies that were streamlined into one and made redundant were removed
•  - A number of trophies have had their objectives/descriptions and/or names updated
• Integrated weapons and armor DLC packs
• - Weapons and armor DLC packs are now integrated naturally into the game; they’re obtainable via research or by purchasing them from merchants as you progress through the game, rather than being immediately unlocked from the start. This ensures overall balance and progression across ME2 and ME3
• - Recon Hood (ME2) and Cerberus Ajax Armor (ME3) are available at the start of each game
• Additional gameplay & Quality of life improvements
• - Audio is remixed and enhanced across all games
• - Hundreds of legacy bugs from the original releases are fixed

One thing that will be sadly missing, though, is multiplayer mode. I've never been a huge fan of that, though, so I'm still pretty excited for this. You'll still be able to get to every end-game option, though, according to BioWare;

"Playing the first two games and carrying over your progress is the most reliable way to get good results in the final hours of the Reaper War. For comparison, if you previously played ME3 with the Extended Cut (which included Galactic Readiness rebalancing), fully preparing for the final fight will be more difficult to achieve in the Legendary Edition." and moreover, "key moments that have been notoriously difficult to achieve in ME2 (and impacted ME3) can now be completed more reliably, leading to better results in the story’s final act." 

BioWare promise that there'll be some more updates on changes, and a deep dive on the graphical changes, soon. Legendary Edition is set to release on the 14th of May.