Numerous reasons. A larger power supply means it is under less stress so runs cooler and (generally speaking) lasts longer, has additional capacity in the event the load it is powering is increased (eg- adding an additional hard drive to a computer), and (generally) has a better capacity to handle high peak or high short-term loads better than a smaller similar power supply.
Bare in mind that switch mode power supplies generally work more efficiently when operated near their upper and maximum load rating, so choosing a power supply that is too big can actually make the power supply less efficient (for the same load powered). Also (generally) the bigger the power supply the more it will cost.
It is all about a balancing act, generally choosing a slightly larger power supply is advisable in most designs and applications (generally).
Would you recommend a 400w psu rather than a 350w psu for about the same price?
The pc is for some gaming, but not a massive amount, and doing work obviously (cough cough).
As for sizing the power supply, one of the key factors to take into account is the graphics card. Modern gaming graphics cards can have enormous power requirements, requiring a 500W or 600W power supply. It really depends on how much 'gear' you have in your computer as to the size of power supply you need, but 400W sounds about right for a standard multi-role computer with an average graphics card.
It pays not to skimp on the power supply. A good quality power supply will generally be quieter and run cooler, extending its life (online reviews will give you a vast quantity of information on the differences between power supplies). Just make sure you clean it and your computer regularly if it is in a dusty area or it will still fail prematurely (as I found out recently).