Crash Bandicoot 2: Cortex Strikes Back is pretty much an improvement over the original in almost every single way.

The level designs and aesthetics are more varied and fun, providing the player with a good challenge, but I believe levels never become quite as hard as Crash 1, which allows this game to be more beginner-friendly, in my opinion.

Crash now has a new move, that being the slide! Doing a slide jump in this game is very satisfying, especially when you're trying to do longer jumps, or when you're just casually running through the stage!
Additionally, Crash also has the Belly Flop, which is performed by pressing the slide button after a jump, and I think it's fine. I found it useful for breaking my momentum in the middle of a jump, but I don't find it as reliable as something like the Stomp in the Boost Sonic games.

I think the bosses are a bit better than last time, not by much, but they are fun to fight, as simple as they may be.
Additionally, there's a bit more story this time around.
I didn't really discuss this during my Crash 1 review, but the plot of last time was that Crash was a failed experiment by Dr. Neo Cortex, and that he escaped the lab, but his girlfriend Tawna, is still stuck in there, and Crash has got to save her from Cortex and stop him from taking over the world with his army of animal experiments.
This time around, Tawna is nowhere to be seen (I wonder why) and Crash has a younger sister named Coco. She doesn't do much in the story, mainly just trying to warn Crash of Cortex's actual plan, which is pretty obvious to see, but considering that Crash is a big dumbass... yeah. Cortex is using Crash to get all crystals, the plot McGuffin of this game, to power up the Cortex Vortex and rule over the world!

The biggest glow-up, I'd say, has got to be the voice acting. Now, in the original game, voice acting was minimal and we didn't hear many characters talking, but when they did... it was meh. Nothing bad per say, but nothing really good either.
This time around, there are more cutscenes, and we hear more of Dr. Cortex, this time being voiced by Clancy Brown, and I love how much character he gives to the mad scientist, it's great!

And that also applies to the game's overall presentation, as the graphics look slighty better, especially Crash's model, and the music is more catchy than the original. Not all of it is memorable, but there are some pretty good tracks in here.

This time around, I actually decided to go for 100% completion, being the first time I ever 100%'d a Crash game, and while it is generally a better experience than the original, but not having to worry about dying, there's probably way more backtracking here than last time.
Now, Crash 1 had its backtracking moments, especially with the colored gems, but this time around, not only can you get a gem by breaking all of the boxes, but also by doing something different, and this is where the Death Routes come into play!

Not all stages have a Death Route, and not all secondary gems require you do a Death Route, but a Death Route is an alternate route of a stage that you get by not dying up to that point. The thing is, a good chunk of stages that have Death Route have boxes in said route and in the main route, which requires a bunch of backtracking and fighting against the game's locked camera to break every box in the stage and get one of the gems.

While this game is an improvement over the original in many aspects, this was the pits, and not really that fun.
But I will admit, I did smile when I finally got 100% completion, especially because it was my first time doing so.

Overall, Crash Bandicoot 2: Cortex Strikes Back is a great sequel to the original, improving on a lot, but still has a couple of snags holding it back from being the best it could be.