Firstly, the Logitech G403 and Razer Deathadder are both outstanding mice. They both have powerful sensors, high durability, and a very long USB cable. These mice are both very sensitive, and are optimized for FPS games. Anyway, here are some pros/cons:
Logitech G403:
Pros:
-Wide range of sensitivity, 200 to 12,000 dpi (cpi).
-2.13 Meter (6.988 Feet) cable
-Programmable RGB lighting
-Removable weight
Cons
-Slower sensor than the Razer Deathadder (RD)
-Shorter cable than RD
-Less buttons (6, instead of 7)
-Buttons not customizable
-USB 2.0, not 3.0
Razer Deathadder:
Pros:
-Razer Synapse 2.0 (Customization software)
-More sensitive sensor than G403
-Customizable Buttons
-Programmable RGB lighting
-2 DPI adjust buttons
-USB 3.0
Cons...