There are advantages either way.
In my experience, making Ubercart (or whatever e-commerce software you are using) your primary inventory system can be advantageous for your support staff. No matter how good your website, you will probably get some calls with questions from potential customers. A common question is about stock levels. Generally the person answering phone questions has a browser open to check order status, shipping addresses, correct payment info etc. . . It is nice to have accurate inventory in the same location.
The advantage to keeping inventory in your accounting software is accurate accounting information. Inventory affects asset calculations, taxes, profit, etc. . . Plus, you will probably generate purchase orders for more inventory from your accounting software. If you have a formula for stock levels, you can usually plug it into your accounting software to automatically determine how many and which items to order.
Ideally you have accurate inventory in both locations, but that is difficult. I have found it best to keep Ubercart accurate, my accounting pretty accurate, and then make monthly adjustments to update the accounting software. But that is because we get a lot of sales calls, and need very accurate inventory due the the small (usually 1-3) quantities we keep in stock.