I agree with some of the above replies that observerships are definitely not as useful as hands-on clinical experience (some would argue that they are useless). But I think it's hard to generalize how useful or useless it is. The usefulness of the experience would depend on where and with whom you do the observership.
For example, I decided to do find my own observership by emailing a lot of different people and I eventually got an observership for several weeks at a private hospital. I was able to shadow a physician with some good connections. My purpose was not to get LORs as they would have been very weak from a hands-off experience. It was simply to get some exposure to the U.S. medical system and being able to put down that I spent some time at a U.S. hospital observing physicians. As it happened, through my physician's connections, I was able to meet with a program director from a nearby residency program who happened to have connections with the residency program where I most wanted to go to. He emailed the PD from my most-desired program to let him know about me. This probably didn't mean much, but I was happy for anything to increase my chances. I think that it's important to try and make as many connections as you can during your experience.
I also think that the value of observership vs externship depends on which country you are from and how senior a physician you are in your home country. I was a more senior physician in my own country with ER and psych experience and I got all of my LORs from the physicians in my own country. Risky, I know, but I got a good number of interviews and matched at my top choice residency program.
If you are from a country with a somewhat comparable medical system (eg. UK, Australia) and you have strong LORs from your home country, you may perhaps get away with an observership. I'm an Australian IMG. But if you're from a different system or you can't get compelling LORs from your home country, then I would think that hands-on clinical experience + excellent U.S. LORs are crucial to have.
Cost is also a consideration. My observership was free (although I spent a ton of time emailing). Externships cost money. In general you should go for whatever level of U.S. clinical experience you need to make yourself stand out as a residency applicant!
