I got FF13 on launch day and played it a ton. I had a lot of fun with the game, but I haven't gone back to play it again since. I did play XIII-2 just a few years ago, and that was an awesome game as well.
In terms of aging: At the time 13 was released, cinematics in games were nowhere near how they are today. Voice acting had been the norm for years at this point, but the actual in-game character doing the speaking did not usually show much expressive animation or lip syncing. Playing 13 at release was like playing the most graphically advanced game up to that point, with solid voice acting, and even the real-time cutscenes were well acted (I assume with motion capture). So that part of the experience won't feel as groundbreaking as it was when the game released.
As for the gameplay itself, the first two-thirds of the game is completely linear. Not just in the sense of the plot, but the actual areas of the game you explore are usually just a single path, and character development is also controlled. This is because the encounters are fixed, so everyone who plays through the game will essentially be at the same level all the time (during those first two-thirds). There is also a ton of cutscenes. That first two-thirds of the game is heavily narrative-based. I don't remember particularly liking the plot, but I do remember that I really enjoyed how amazing everything looked in the game, and I liked the cast as well (Sazh being my personal favorite).
Once you get to the open world, that's when it becomes a game where you can power up your characters to do insane amounts of damage and take on the big bosses. Leveling up is similar to the sphere grid in it's style, but it's much more linear. There are a few branching paths to take on the grid, but eventually you'll want to get them all anyways. (I never finished the leveling process myself. IIRC, you can get about 90% through the leveling process, and then out of nowhere those last few nodes start requiring insane amounts of exp. It was one of the last things I was missing for a platinum, in addition to one that required having every accessory in the game.)
Overall, I really enjoyed playing through the game back when it was released. It has a very unique sound and tone for an FF game, but it's enjoyable.
I just realized I didn't really mention the combat. I thoroughly loved the combat system, and I want to explain how it works (because it's brilliant). Absolutely what made this game awesome for me was the combat, and why I stuck through the post game to finish every last hunt. The combat system is quite simple in theory, but it's mechanics allow for some very satisfying strategies when fighting enemies. Your characters each have a role (which is essentially a class), and as you play through the game you unlock more of them for each character.
When you enter combat, the three characters you use in battle determine your "paradigm". I want to say that there are a total of six or seven of these roles in the game, but every unique possible combination of these roles that can be made with those three characters has it's own "paradigm". For example, the two damage dealing roles are "ravager", and "commando". When a ravager attacks an enemy, the enemy's stagger meter grows faster.
The stagger meter is a gauge that determines damage bonus. Different enemies have different thresholds and resistances for how much their meter will need to build up versus how long it takes before the meter depletes. When the stagger meter is empty, you deal base damage (100%), but as it fills, this damage increases up to 999% for some enemies. Others may stagger at maybe 300%. When they stagger, the enemy remains in a state where they cannot attack and you are free to continue damaging them to boost the percentage until it resets back to 100%.
Going back to what I said before, ravagers build this percentage. That's their role. They don't do a ton of damage on their own, but they build the damage multiplier. Commandos, on the other hand, deal tremendous damage, but do very little in terms of building the stagger percentage. However, commandos are necessary because commandos prevent the stagger from diminishing. If a group of ravagers all attack at once, the stagger meter will not sustain itself. You need a commando against most enemies to maintain the level of stagger, preventing it from resetting back to baseline.
So the early game strategy that you will quickly figure out is to build up that stagger bar with maybe COM/RAV/RAV, and then when they are staggered you have to consider how to best maximize damage. Perhaps switch to RAV/RAV/RAV for a few seconds to boost that percentage even more, and then switch to all COM/COM/COM to deal damage until stagger resets.
All of that strategy exists with just those two roles I mentioned, but the other five or so roles will allow for buffs on your party (SYNergists), debuffs on the enemies (SABoteurs), heals on your party (MEDics), and defensive abilities (SENtinel). I think that's all of them.
Probably way more information than you wanted, haha. But the combat kicks ass.