For a break-down of the series:
Fatal Frame 1 has a pretty straight-foward story and may be the hardest game in the franchise due to some imbalance of how difficult some ghosts are, it's set in one single location that slowly opens up over time, but in my opinion is one of the creepier titles in the franchise. It's rough around the edges in some ways, but some of that roughness adds to the appeal (the game having sudden difficulty spikes does make the fear of survival of what might be coming up increase XD; ).
Fatal Frame 2 is actually by far the easiest entry in the series, but it has an interesting location, a bit more of a dramatic story, and some fun ghosts and atmosphere, and generally is the most popular due to its story and setting. Story isn't really surprising, but well told, and there's some fun J-horror style ghosts in it.
Fatal Frame 3 I think is often under appreciated, it introduces the multiple characters for chapters thing, and features a story about a place appearing in people's dreams. As such, you hop between the 'haunted' house in your dreams, and your apartment, that's slowly growing creepier and creepier. I like that mechanic, and in my opinion some of the creepiest ghosts exists in the third game, and it has my favorite ending of the four games. It also started the longer FF-game thing, I think FF3 took me 18-19 hours to beat taking my time (while the first two are about half of that). I think FF3 has my personal favorite story in the series, and FF3 has the most hidden scenes that are easy to miss in my opinion.
Fatal Frame 4 I've concluded might be my favorite, which is weird to say since I think I also have the most problems with it, but I think it has the most interesting and creepy setting with interesting and grim rooms, and something about it I find really appealing, I can't quite put my finger on it, but I really enjoyed exploring the location, and some of the moments and scenes in that game are the best in the franchise in my opinion.
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I have not played FF5, but honestly it's what I fear might happen. Not with the game, but the reception. FF5 basically sounds like critics are taking issue with what is also present in the other entries in the series. Some are loving it, while some can't appreciate it being old-school designed. A lot of horror fans are upset that horror games like this don't exist any more, it's the reason why RE, Silent Hill, and the like changed, a changing market. FF has stayed mostly the same over time, it's had changes but it's still very much old-school, and the 'flaws' people are calling out in the reviews are true of the rest of the series as well. But those 'flaws' are just in personal taste, and some will actually enjoy them. Others won't, but those who like older-school horror games or the older horror games, or FF3 or FF4 even, what is called out here is echoed in those games as well, so basically it sounds more like the game wasn't in the strike-zone of those who've played it.
That's fair, fine, and it's why I believe reviews are so all-over the place, but it does mean it's less likely people who like these type of games are going to see many of them over here again, which is a shame. Horror fans I know who have played the game are positive on it, and I feel this just shows it's a niche audience type thing, which is a bit saddening.