Private stings are less reliable because there's no guarantee the suspect's rights weren't violated or that entrapment didn't occur (by that jurisdiction's laws, not the layman's interpretation of the term), there's no reliable "chain of custody" for any evidence obtained, and often in a court's eyes, all of the evidence gathered is basically just hearsay (even chat logs, phone and video recordings, etc.) because no "official" law enforcement was involved in collecting it. That is to say, the suspect wasn't IM'ing a police officer acting as a decoy, talking dirty and sending naughty pictures. Chat logs are trivial to fake (they're just text) and a private citizen's word that "these are totes legit" often isn't good enough.
The other big problem with private stings is they're fucking dangerous. Big-budget investigations like To Catch a Predator lured suspects to a controlled environment that was carefully set up to keep everyone involved safe. Lots of physical security hiding in rooms with low lighting, hidden cameras everywhere, a non-aggressive and non-threatening confrontation that quickly ended in the suspect being surrounded by a camera crew, police waiting to "spring the trap" when each suspect left the house, and so on. I think they only ever went out "on location" for one sting, and that was only because they'd literally busted the absolute bell-end the day before and he went straight home to arrange another meeting with another girl who also happened to be yet another decoy by the same sting operation (lol).
These vigilante types, on the other hand, cheerfully go out into public places (often as a group) to aggressively confront suspected pedophiles. They get right in their faces, call them names, threaten them with arrest and ruin, follow them if they try to leave the area, often times try to physically block or even detain them, and rarely "break off" if their target clearly warns them to leave him alone. Do that in America in some places and you're liable to end up staring down the barrel of a gun. Everywhere else you're risking an ass kicking. And either way, you'll generally find the cops unsympathetic because you just rolled up on some dude and started flexing on him. I've actually seen these vigilante groups post videos of confrontations that include police interactions at the end where the cops literally say "wait, so you're not law enforcement? WTF are you thinking acting like this? You could really get hurt!"
Since those confrontations practically never result in an arrest of a suspected nonce, they just go home knowing that people are watching and they've likely informed the police, so the nonce knows to go "under the radar" again for awhile so potential investigators lose interest and move on. If these vigilantes would just gather chats, emails, photos and videos sent by the suspect and then turn that in to police, actual law enforcement could then actually start watching the guy for awhile as he operates without him knowing he's being monitored. Direct confrontations just make the nonces harder to catch.
Productions like TCaP did their homework (at least after the first special aired) and contacted law enforcement agencies well in advance of setting up those stings. They collaborated with police departments to run the stings in a way that (usually) gathered enough reliable evidence to get convictions. They also made sure that host Chris Hansen always made it clear when he confronted each target that he wasn't a police officer or any kind of law enforcement official, and made it equally clear they were free to leave at any time. He never threatened violence or arrest, and never assumed any threatening posture (or even raised his voice, except for a few times when he couldn't help but sound incredulous at some ridiculous excuse someone gave him during the confrontation). And nobody in the production ever physically blocked someone from leaving. They also never performed a direct hand-off to police; they always just showed the target the exit, and had the cops waiting around the corner or in the garage or whatever. They cooperated with police, but they didn't get involved in making arrests.
If you've seen all the shows they aired, you'll notice that after the first couple of stings they ran, the group they worked with ("Perverted Justice," I think) started asking their targets to bring specific items with them to the in-person meetings they arranged. Condoms, of course, but also something like a pizza or a plushie or a "present" or a specific type or brand of beer/alcohol. If the target showed up without those things, they could usually still get a conviction, but if the target did bring those specific items, it served a dual purpose -- it proved the person who showed up was the same person who participated in the chats, and it showed intent. It's pretty hard to explain why you'd just randomly show up at some 13-year-old girl's house with a plushie and a box of condoms in your pocket unless you were chasing some underage booty.
Even with all that preparation and care (I personally think they did a genuinely good job, actually tried their best to get it right and weren't just chasing ratings), there were plenty of instances where men caught in those TCaP stings either didn't get prosecuted at all or ended up being acquitted. It was almost always because of entrapment arguments or disputes about the reliability (and admissibility) of gathered evidence. And in a few cases I think the DAs just decided it wasn't worth prosecuting because there wasn't an actual victim.
So even with all that credibility, they don't always get convictions despite clear guilt. And private stings can't get anywhere close to that level of credibility.
