Which is the better module for shopping cart?
From the sounds of it, you actually want a whole e-commerce system, not just a shopping cart.

Ubercart will do this for you, but the general trend now is to go with Drupal Commerce (project page | Commerce homepage).

Both modules will allow for shopping carts, as well as integration with a variety of payment service providers.  I'd personally go with Drupal Commerce.  It seems a little more difficult than Ubecart at first glance, but once you get over that you'll realise it is much more flexible/powerful.

Try using the Commerce Quickstart installation profile to get yourself familiar/started with it.

There are a lot of good videos for Commerce as well such as Selling Content with Drupal Commerce using Content Access and Roles from the Commerce Guys.

Lastly, there is a blog post here that weighs up the pros and cons of each system (although it is from 2011)

Edit:

You might find the getting started guide useful also.