350W Power Supply vs. 600W Power Supply

I just purchased a new desktop pc (specs below) which has a 350W power supply installed in it. I have a new 600W power supply sitting on my shelf, and would like to know if there would be any advantages to installing it, if so what are the advantages?

This is the 600W power supply: http://www.ultraproducts.com/applications/searchtools/item-details.asp?EdpNo=3255393

Processor  Intel® Core™ i7-2600 Processor (3.40GHz)  
Operating System  Windows® 7 Professional 64-bit; Recovery Disk Included  
Memory  12GB DDR3 Memory (4 slots, 32GB Max)  
Hard Drive(s)  2TB SATA Hard Drive  
Optical Drive  22X DVD±R/RW  
Graphics  Integrated Intel® HD Graphics (Dual monitor capable)  
Audio  10 (7.1+2) channel Intel® High Definition Audio  
Card Reader  19-in-1 Multiformat Card Reader  
Networking  10/100/1000 Mb/s LAN  
Input  USB Keyboard & USB mouse  
Preloaded Antivirus Software  Symantec Norton Internet Security 2011 (30-day trial)  
Ports  (6) USB 2.0 - 2 front, 4 rear; (2) USB 3.0 (rear), (1) RJ45 LAN,(5) Audio, (1) S/PDIF, (1) HDMI, (1) DVI ***NOTE: DOES NOT INCLUDE 15-PIN D-Sub / VGA PORT. To connect this PC to a display with a 15-pin VGA connector, a DVI-to-VGA cable adapter (sold separately) is required.  
Expansion Slots (Total)  (2) PCI Express*2.0 x1  
Expansion Bays (Total)  (2) 5.25" Exposed, (1) 3.5" Exposed, (4) 3.5" Hidden  
Dimensions  (HxWxD) 13.9" x 7.1" x 16.9"  
Weight  30lbs  
Warranty  1 Year Limited Parts & Labor Warranty  
Support  Lifetime Toll Free 24/7 Technical Support!  
Power Supply  ATX 12V 350W