All kind of achieve the same thing, but in different ways.

Pi-Hole is the completely free way of doing ad and tracker blocking at the DNS level. Free as in free beer and free as in free speech.

AdGuard is free as in free beer but not as in free speech.

Both solutions mentioned above have to be self-hosted.

NextDNS is a managed service for which you have to pay a (very small) monthly fee for. The advantage is that - once setup - it pretty much just works (exception being custom updates to filter lists, but that applies to the other two as well). What's cool about that is that it's reachable from outside your local network, so you can use it on your phone or whatever even when you're not at home (they offer apps and profiles for easy setup). You can expose your Pi-Hole/AdGuard DNS to the outside world, but this has some caveats and probably higher latency/worse availability.

Opinions differ when it comes to privacy, but I'd say they (NextDNS) are trustworthy/not selling your data as this doesn't seem to be their business model. Obviously, with Pi-Hole you don't have to trust anyone (except the code authors unless you study the code yourself), so when in doubt Pi-Hole wins in this regard.

Be careful when setting up either of these as the default DNS service in your home network, especially when other users are in your network, as the default configuration of either of these will break some websites, services and apps to stop working and you (the admin) would have to handle the errors your users are getting by adding exceptions and/or different filters. The good news is that there are more conservative filter settings available that will still block most ads and trackers while being way less likely to break anything.

Pihole is most popular among self holsters. It has nice GUI, it’s capable and its solid. It’s basic in sense of DNS features. You need to use config files to customize from terminal and even then it’s limited.

Adguard in my experience has more advanced blocking features. DNS also allows you little more flexibility like wildcard records. You can have separate config for different clients (like guest/kids network blocking)

NextDNS is SaaS only. It has most advanced blocking features but free account only gets you limited queries monthly. You can choose to keep your logs on specific servers or not to keep at all… from privacy perspective it’s arguably worse because you have to trust another company but it’s a good middle ground. Self hosted still needs upstream DNS but it could be tunneled through VPN which would anonymize traffic. NextDNS is upstream dns and it can’t distinguish internal network source.

I would throw zenarmor to the mix https://www.zenarmor.com/. Paid home license costs 10$/month and allows 3 different profiles. It is more advanced as it sniffs all network packets and not only DNS. It’s not replacing dns. It has great reports/dashboards.

For best DNS capabilities I would recommend technitium https://technitium.com/dns/. It’s free. You have gui, dns blocking and full DNS capability with some advanced plugins. It’s not as fancy for dashboards like pihole or Adguard.

You would use combination of solutions and nextDNS could be your upstream if you don’t mind paying them. If privacy is your thing you want to have more generic upstream that everyone uses like quad9.

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.

NextDNS seems cool but it looks like it is for-profit and proprietary software, which is a deal breaker for me. Even if their "free" tier were good for me, for now, the price and my privacy would always be subject to the whims of a company who is going to be trying to get money from me. Fuck that.

Just to clarify, you don't need to install an app or extension to use AdGuard, you can just use its dns servers. I use their own dns for my phone, so that it works everywhere, but I use my self hosted AdGuard instance at home.

I haven't needed to change anything in the filters yet, but by self hosting, I've got the option if it's ever needed.

Adguard

safing.io block kernel-level DNS, so no one is bypassing DNS and more stuff... and it is free and open source... I don't understand why people even talks about Pi-Hole unless it's for your smart-tv, which then makes sense, but your phone or laptop will not work once you get out of your home network, and your PC programs can bypass it easily.