I use Pi-Hole and works great. I’ve heard about AdGuard and seems the same thing as PiHole
Only if you're talking about AdGuard Home, then yes. When you talk about AdGuard you usually just mean the adblocker app which is something completely different.
I used all three of them. While AdGuard Home has some nice features that Pi-hole doesn't, it in my experience has much more problems and has been unstable on some updates. So since you prefer stability for your DNS server I'd recommend Pi-hole over AdGuard Home.
NextDNS doesn't need to be self-hosted because it's a service on the internet. The disadvantage is that you are offered a list of blocklists from which you can choose but unlike Pi-hole or AdGuard Home you cannot add more lists. But they offer many lists so that's not a big problem. If you need more than 300k queries a month you need to pay for their service. But since NextDNS is a service on the internet it means that you can use it on all of your devices no matter where you are.