There is nothing wrong with the classic system you have. Valveman is the owner of a company that sells an alternate system "CSV" (Cycle Stop ValvesŪ is a registered trademark) is a branded system that uses a smaller pressure tank. You can click on his link for the positives which include use of a smaller pressure tank.
Your understanding is true. In some systems the bladder holds air, and the tank holds water. In other systems, the bladder holds the water and the tank holds the air. I think bladder holding water is more common. http://www.flotecpump.com/residentia...faq_tanks.aspx
Your tank allows the water to build up. Your tank will hold about 30% of the nominal capacity between pump turn off until the pressure drops enough for the pump to turn back on. Your tank should have been pre-charged with air to about 2 PSI less than the cut-on pressure for your pump. That pressure would be set when there is no water pressure. Since you let air out, you should use a tire gauge and a pump after you have turned off your pump and let the water pressure drop by opening a faucet until flow stops. A compressor is much easier, but even a manual tire pump can do the job.
I would only replace the if there are symptoms. The tank can hang upside down, but remember it is heavy when full. So it will need heavy duty mounting.