This question largely comes down to what your plans are for you bike! Both these set ups are tried and tested and there is no right or wrong answer here, so it really comes down to what type of adventure you want to lead.
Panniers are long estabolished and are the most well known method of taking your things on the road with you. A classic, road touring set up often includes two large panniers at the back, and two smaller panniers in the front, both attached to racks which are mounted on the bike. Beyond this, people will often will have a drybag attached to the top of the rear pannier rack, and a handlebar bag for easy access to maps, snacks and other essentials.
This set up is great as it offers the rider lots of storage, and has lots of flexibility when it comes to carrying a few days worth of food. It also allows the rider the ability to quickly remove their bags from the bike, allowing them to take their items with them if they're stopping for an extended period. These bags can also be handy for day to day commuting, and allow the rider to change amount of carrying capacity they need by simply adding or removing bags. They are also usually waterproof, meaning that you can be confident that your cargo will get to where it needs to be compltetly dry. The main downsides to panniers are their compatibility with different bikes, their weight and their size. This is when bikepacking specific bags begin to shine.
Bikepacking bags have been around for a little while but have only really gained popularity recently, as more people are looking for ways to go for off road bike trips. Unlike panniers, which require front and rear frame mounted racks, bikepacking bags mount directly to the frame of your bike with no additional hardware. This is good for a few reasons, one being that a bikepacking set up is lighter, and have less wind resistance due to them being less prominent on the bike. They are also thinner when attached to your bike, allowing you to squeeze through narrower gaps then you could with panniers. The bags are also more evenly distributed around your bike, making off-road handling better. In addition to this, these bags are compatible with practically any bike, as they don't require any mounting points on the frame in order to be attached. This means you can attach these bags (carefully) to a full-suspension mountain bike and go places that you couldn't dream of on a rigid, pannier based touring setup.
A regular bikepacking set up includes a saddle bag, handlebar roll, some sort of frame bag and a top tube bag and/or snack pouch for getting to little things on the go. Some drawbacks of bikepacking bags are that they can be difficult to mount and remove from the bike, making them less practical for commuter use. These bags also are not always waterproof, so if this is a concern for you then double check this when selecting your bags. They can also be harder to get things out of for this same reason. The main drawback for a lot of people, which also is a benefit a lot of the time, is that they have significantly lower carrying capacity then a pannier set up. This means that unless you have an ultralight camping set up and freezedried meals, it can be tricky to fit all your things onto your bike. This obviously doesnt matter if you're staying in accomodation that has catering, but is definitely something worth considering. However, this also plays a massive part in making the bike more nimble off road, as the lighter overall package means that your bike handles more like it would without any bags attached.
If you want the best of both worlds, you can also exists between these worlds. If you have a hardtail mountain bike you can run a small set of panniers on the back in combination with a full set of bikepacking bags. If you have a rigid bikepacking/gravel bike, you could also run a small set of panniers on the front, combined with a regular bikepacking set up for a more planted from end. These set ups would allow a halfway between these two options, meaning you have expanded carrying capacity, with more off-road capability.