I'm a UI/UX Designer and I design websites for a living (I do a lot of web applications).
A website built using competent designers and developers shouldn't have any of the issues posters here are describing; if you have people that know what they're doing, you should have a user experience that scales well between desktop and mobile and won't make you feel frustrated, or like you're missing things. The problem is, everyone and their mother thinks that they can just read some tutorials and be masters of responsive design and user experience, and those are the people that are responsible for the large number of crappy mobile sites that you see.
It takes a little more thought than, "I'll just use Bootstrap and make my site work on phones"; you have to really think about the use cases and think about user needs. For example, if I'm looking at a restaurant website on my phone, I likely don't care about pictures or the owner's story... I want the hours, address, menu, and maybe a link to OpenTable. A lot of sites just try to cram all of their desktop version's content into the mobile one, which obviously doesn't work because of the screen size.
In my professional opinion, here are a few sites that I think are crafted well and provide a good mobile experience (Protip: Resize your browser window a couple times):
http://www.unitedpixelworkers.com
http://www.squarespace.com
http://www.starbucks.com
http://www.wordpress.com
In summary: Yes, there are a boatload of terrible mobile sites out there, but I think people are starting to get with the program. Expect better quality mobile sites over the coming years.