Part 1's Joel is limited to the same basic moveset featured in the original game rather than the faster gameplay of Part 2. However, more here has changed than I expected. Animation, camera work and even enemy behavior has changed between the two versions.
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... the core shooting mechanics feel more in line with Part 2 - camera position, weapon animations and hit reactions are all far more polished. The motion blur, smoother, slower zoom and aiming position feel like the second game, while the animation of firing the weapon is unique to both prior versions but is closer to Part 2 than the PS4 remaster. (...) The basic moving and shooting action has been overhauled and Part 1 feels like a nice hybrid between the two games.
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When you combine this new AI behavior with the improved shooting mechanics and more reactive environment, it does feel suitably different. This represents much of what Naughty Dog refers to as 'improved gameplay' and this description does seem accurate.