Venous punctures are typically done for regular blood work such as getting a CBC (Complete Blood Count) and are often enough for regular access - medications etc. Venous access is also used for things such as PIC lines (IV catheters that run almost all the way to the heart).
Arterial punctures are often done for getting a "blood gas". This is used to measure gas levels in the blood (such as CO2 and O2). Arterial punctures can also be used for establishing an arterial line in a large artery such as the femoral.
To sum things up a bit: although venous punctures are more common and often enough; arterial punctures are often needed for more specific testing.
For additional information, please visit MedScape and LabCE. I hope this information is helpful to you, if you have any additional questions, please let me know.