'Abate' is when something becomes less serious and intense whereas 'reduce' refers to a decrease in the amount of degree.

'The risk of infestation has been abated by the new drug.'

'I used to eat a lot but now I reduced my portions.'

The difference is that when we use 'reduce' we are speaking of something in the exact same QUALITY but in a lesser QUANTITY. However, for abate, it is the QUALITY of its intensity that has reduced and not the QUANTITY.