Practically every shopping cart out there has basic (or advanced) inventory management functionality. I have been evaluating a dozen e commerce platforms lately and Big Commerce is certainly a good choice. It allows for a lot more growth than some other carts and has some very advanced features that are still simple to use. The one glaring thing that Big Commerce is missing in my opinion is a customer rewards program. They have been looking into adding one for more than a year and I don't know why they haven't pulled the trigger. More than 100 people have requested that they add it. It also tends to be a cart that is better suited for businesses located in North America. All in all - especially for relative new comers to e commerce - I would have to rate Big Commerce as the best all around platform available right now.
A lot of this also comes down to what country this website is going to be marketing to. If it is somewhere like Australia, for instance, Big Commerce will not do at all. They would be better off with Core Commerce, which offers more well rounded international shipping, language and currency options.
If they plan on integrating several related websites that all sell the same merchandise but are optimized around different keyword sets and he wants to control inventory for all of the sites pulling from the same inventory, AmeriCommerce would be the best solution. Americommerce is probably the most flexible and robust shopping cart I have ever come across. Although a relative novice could get things done in it, more advanced users can do practically anything they ever dreamed of with that cart.
Personally, I wouldn't even consider Shopify. It is far more expensive than it should be for what it is. Magento is a very good cart if you don't' mind getting your hands relatively dirty. People with HTML, CSS and PHP along with programming skills tend to favor Magento. If your client is not up on that kind of stuff, I'd steer clear of Magento; it's not real newbie friendly.