The first one, they asked me to solve an incredibly complex math problem that I had no idea about so I struggled with it for 5 or so hours before giving up. Probably good that they didn't give me the job; if they were expecting me to know the level of math they were requesting then I would have had a pretty bad time. So I guess the test worked in that regard.
The second one interview at a different company, they gave me more moderate questions after a phone interview- mostly questions testing knowledge of a specific language. When I asked how long it would take, I was told "you have a deadline of 8 hours from when you download the zip file to when you turn in your code, expect it to take the entire 8 hours". That was probably the most stressful 8 hours of my life, way worse than any whtieboard interview would have been. I didn't look away from my computer once the whole time, did not let myself get up to eat, go to the bathroom, or anything. My girlfriend was in the room and tried to console me while I was doing it and stressing out and I ended up yelling at her to be quiet because I was trying to hard to concentrate. I finished the last problem about 10 minutes before the deadline, zipped the files up, and sent it to them. I never heard back.
Favorite interview I've ever had was a combo of a live coding session and a phone interview. They used an online tool that they gave me a link to that had syntax highlighting. The interviewer on the phone could see where I was typing and could highlight stuff etc. Think google docs, but for coding. They asked me to write some algorithms, then asked me to re-write them recursively, then asked a bunch of questions about the limitations of the algorithm, cases when it would be used, etc. It was fun, not stressful in any way, and the interviewer even taught me some things along the way! I feel like they got a really good picture of my thought processes and my personality so they could accurately judge if I would be a good fit on the team.
Paying somebody to do the take-home coding assignment and paying them would definitely help alleviate some of the stress, but I'm still not a fan of the format. You don't know how long it took the person to make their solutions, and you don't get a good idea for how they work, only what they can do (both are equally important, in my opinion).