Any of the Intel ET or ET2 variants should work in either the x16 PCIe slot or the x16 (wired x4) slot. However, I don't have one of these desktops that I can use to confirm compatibility. The connector on the adapters is PCIe, x4, which will definitely plug into your x16 slots. I have an Intel desktop where I regularly plug in server adapters into the desktop's second x16 slot. (The first x16 slot has my graphics adapter.) I would be surprised if you had any trouble using these network adapters in your Dell system.
You can compare Intel gigabit server adapters in the product catalog at http://ark.intel.com/products/family/46829. You might want to consider the most recent dual port adapter, the Intel® Ethernet Server Adapter I350-T2. Released in 2011,this dual port gigabit server adapter hasall the latest design improvements including improved power management. Both adapters have great virtualization support, so either adapter will be a good choice.
Thanks a lot for the clarification - it's very much appreciated. Also, thanks for the guidance on the I350-T2. I will definitely look into this option as well.