TL;DR
Axiom Verge is a great modern take on the retro metroidvania.

INITIAL THOUGHTS:
Maybe it's the nostalgia for the retro aesthetic, maybe it's the simplicity of exploring the world of a metroidvania, or maybe it's finally having a game that feels natural on my steam controller that isn't about car-powered soccer. Whatever the cause may be, the ten hours I logged on my first playthrough were all incredibly enjoyable and even though I do have a few issues with it you can't get a better modern metroidvania experience than with Axiom Verge.

PROS:
Starting from the very basics, the game looks amazing and goes to show that incredible worlds can be build without a million-dollar art budget. The retro-aesthetic perfectly matches the retro-style gameplay, creating the perfect casual atmosphere to enjoy. The world is incredibly interesting which means backtracking (you will do a lot of backtracking) rarely feels like a chore, and by the time you do have to return to an area you usually have some new ability that opens up a little bit more of a room you thought you'd cleaned out an hour ago. The game is also full of items, weapons, lore, and bonuses that are incredibly satisfying to find, so if you're a completionist you have your work cut out for you, but nothing quite beats the feeling of gaining a new ability and using it to explore more of the world. The sound design of the game is excellent as well, the background music is fantastic and the sounds your abilities make when you use them are incredibly satisfying. Sound design often gets overlooked but doing it well can make any game better, and Axiom Verge does it perfectly.

CONS:
These are all minor flaws I noticed while playing. If you play with a joystick controller you have to double-tap the stick in the same direction to perform some abilities, an action that always felt a bit awkward to me especially during more delicate platforming sessions. The boss fights are fun and enjoyable but most of them can be beaten with relatively little work if you use the right strategy, which can make an awesome fight less exciting, but you by no means have to play them that way. Lastly (and this is about the more fundamental design of the game), Axiom Verge rarely leaves you lost with almost no idea where to go. That may seem like a pro, but to me the metroidvania category is all about exploring a world and discovering new things on your own. While Axiom Verge never explicitly tells you where to go your options are often extremely limited, forcing you down a singular path. At about the halfway point the game starts to open up a bit, leaving more room to explore, but the initial few hours seem incredibly scripted for an otherwise well-done metroidvania. In talking with other players not many even seemed to notice this railroading so maybe this is a moot point, but from a design perspective it's definitely there.

YOU SHOULD BUY AXIOM VERGE IF:
-you enjoy older metroidvanias and are looking for one with modern polish
-you're looking for a casual game to play at your own pace
-you're a game designer and want an example of how games can silently guide the player
-you like games with lots of collectables
-you're looking for a new game to speedrun (there's a built in timer should you choose to use it)