Typical price for 20-hour puzzle hunt is about $3-5 per person. Escape room costs 1 hour for about $30. The room is probably much better done, but I would bet you would have more fun puzzle solving in a more traditional puzzle hunt.
Just came back from a 5 day vacation in Prague. We went to 5 different escape rooms during that vacation. It comes out to about $10 a person for a group of 5. Money well spent for an intensive hour of fun.
There is a lot of stress involved in the puzzle hunts as well -- you have to solve the toughest puzzles at around 3am in the woods, some even in November. Struggling with fatigue (personally at around 8am) and not giving up is a big part of that, and if your team wants to be among the top 10, speed is a very big issue.
The Czechs who like puzzle hunts (such as me) will likely prefer them over room escapes as they are all cheap, non-profit, community events with a good atmosphere, whereas the room escapes are more of a product that aims at the workforce (many room escapes talk about team building in their brochures) and the prices reflect that.
The main downside for the foreign audience is that most Czech puzzle hunts I attended required fluency in Czech in a non-trivial way -- encoding messages in proverbs, conjugation, wordplay and so on. It's tricky; foreigners don't know about our puzzle hunts (it's a purely local custom), so they do not want to attend -- and the organizers feel that having them in Czech is enough.
I'm Czech and I've never heard of such thing, but again, I've never heard of escape rooms either. I had no idea this was so big here.
For a intellect based hobby event for Czech-speaking people, I'd say those numbers are pretty big.
I guess they are mostly being done by social groups for their members, not for customers.
If you walked up to someone in the street in the US and said 'puzzle hunt', many would not know the word, but if you said 'scavenger hunt with puzzles', they would get it right away.
I was also curious if that comparison was at all accurate.
Regarding terminology, I struggled with that too, to explain to my american coworkers. I think "puzzle hunt" is probably the best translation of Czech original term "šifrovačka" or "šifrovací hra" (which would precisely mean "cipher game"). I have never participated in a scavenger hunt but my understanding is that it's a slightly different game.