Conceptually speaking, every smartphone today can be called as a mini computer, as it can perform almost all of the computing tasks. But as the physical size of the smartphones is very less in comparison to a computer, there would be some basic difference in the way it would work.
The other differences would be the size of RAM, the ease of operation and the screen size.
While browsing the internet, the way you can access multiple tabs, won't be the same in a smartphone. The way you scroll down would also not be the same in both the devices.
As the keyboards are also different in kind, things would appear different.
Now coming to the websites, each of them needs to have two different versions to wear a user-friendly look and interface. In most cases, the sites have a desktop version and a mobile-friendly version.
So, what you are talking about, that is the missing components that you find in mobile,m would be the same whichever mobile you choose to use.
But if you want a portable device that would work like a computer, but be smaller than a laptop, you can try using a tablet instead of smartphones, or even notebooks or netbooks are good options as far as portability and price are concerned.
So, there is no point in suggesting you any mobile or smartphones on this ground.
