There are at least three different methods to carbonate beer in kegs.
You can can/bottle off of keg too, also a few different methods to do that.
More consistent carbonation levels are a benefit of kegging. Plus you can easily adjust the carbonation level of a beer in keg. Not possible with bottled. You either got it right, or not, with bottles.
No concerns about bottle bombs with kegs (corny kegs are rated to 135psi).
No concerns around getting 100% seals as you can have with bottles.
I started with bottles (swing top because I couldn't get the crimp on type to seal properly, reliably). I then went to kegging pretty early on. I've used the Blichmann beer gun for a long time to bottle from keg (direct form the keg, not via tap) and now have the Tapcooler item (setup for cans).
I'm also currently using the keg carbonating lid from MoreBeer to get the beer carbonated in about 2-4 days. Without having to roll/shake/purge/etc. like you do when attempting to rapid carbonate otherwise.
Closed system transfers are also wonderful to do. Plus easy since you'll probably have the items needed already when you set up for kegging. I ferment under pressure, so there's zero issue doing the closed transfer method. Fermenting under pressure also means my beer is partially carbonated before it moves to keg.
As with most things brewing, ask 10 brewers and you'll get at least 10 [slightly if not more] different ways to do things.
You can do closed transfers with a keg. This is huge with the trend to heavily dry hopping beers like NEIPAs (hazy juicy beer). Assuming you have a fermenter that can handle the pressure at use ball valves stems you can use keg the beer in a low/no oxygen environment this preserving the hops (ie preventing oxidation). Of course this is a bit more advanced.
IME, CO2 leaks are easily avoided by ditching the worm clamps and using oetiker clamps (or ear clamps). They grab all the way around the tubing, unlike worm clamps. They are single use items, but they're strong enough that you don't care. I keep plenty on hand for the gas and beer lines, in case I want to change something.
I switched over soon after setting up my first keg fridge due to CO2 leaks. Zero leaks at those points since I did that.
With the right hardware you can also have more than one CO2 level for your beverages. Want a stout at lower CO2 volumes, but also an ale at higher? Dual body regulator will do that. Or additional regulators between the feed and each keg. The possibilities are endless for that.
With Kegging, you will need more equipment. equipment - keg, co2 canister, co2 (i have a 20# tank, 32 dollars to fill, will last a few years, depended on how you use it, recurring expense)hoses, clamps, regulator, a designated cooling device (i.e.... kegerator, keezer), kegs get heavy when full, if your line leaks, you loose all your beer(one of my picnic taps dropped, and opened up - 4 gals of beer down the drain), you forget how many pints you have had ( especially when you do top offs)
With bottles it is - bottles, caps (recurring expense), bottle capper, bottling bucket, priming sugar( recurring expense). bottle bombs, 30-45 min to fill, cap, clean up.
upside to kegging - 5 min to fill the keg and in the fridge to carb,you can fill bottles and take them with you(and drink from the bottle with no worries)(you already bottles and caps and stuff, so why not use them). you can fill growlers, howlers. you can have carbed up beer faster ( i do set and forget, so still 2 weeks), clear beer. and so many more....
Upside to bottes- no dedicated cooling system (regular fridge would be fine for a 6 pack with out taking up to much space), easy to keep track of how many you have had. can store lots of different flavors without taking up to much space. (stackable cases).
i have 5 kegs, one is dedicated to Cider, I rotate 3 of them with beer, 1 is back up/ when I decide to brew more and rainy days,
You don't save a load of beer in bottles, thinking that will be good to try later when it's improved. Then sample your archive and find that what went into the bottle has deteriorated.
The plus side of bottling is you know what to do with the bottles, once you start kegging you then find the bottles a PITA but can't seem to let them go!
A while back, when I wasn't brewing, I got rid of most of my bottles (swing top) since I wasn't using them. I kept a box of them just in case (500ml). Until I got setup for canning I would fill an occasional bottle off of keg for people, or to take someplace. Now that I'm canning, we can at least one keg of the batch (canned all of the last cider we made, almost 6 gallons into 16oz cans).
Most of my kegs are 3 gallon sized. It made more sense when I had the fridge for kegs. I could fit four into a 10 cubic foot fridge/freezer. Now, it just means I can easily lift them into the keezer. Getting 5 or 6 gallon kegs in, isn't as easy. But it's not impossible. Another benefit of the three gallon kegs is I can keep one and can the contents of the other.
Another benefit of kegging is you can move the beer from fermenter into keg in a closed system. Which means [pretty much] no chance of oxidization or infection during the transfer. Of course, you need a fermenter that can handle being pressurized to do that.
I've got to stop being Frozen and " let it go ". I only need the bottles for giveaways and samples now. Have got a really good counter pressure bottle filler that's mess and hassle free. Closed transfer, gas harvesting and keg flush outs without oxygen all become easy with the pressure fermenter plus bottling the excess straight from the fermenter.