Do you prefer to fix water pump or replace the broken pump?

first replace the broken pump after that fix new pump.

That depends on the problem at the pump, and the pump type and its size, capacity, head, etc, also the cost is a very important factor

so these are the two important factors to decide on such situation which are:

1- the type of the problem, if it will get the pump back to work and for long run or not, so if this problem can be fixed and will get the pump reliable at working again, fixing is the right decision

2- the cost of the pump, as there are a lot of pumps very costy to replace, so repairing it and replacing the broken component is the right decision

but if the broken part can't get fixed nither available as spare part, and not reliable to change, then we must change the pump with a complete new one 

If fixing is cheaper and can guarantee a reasonable lifespan, then I'll opt for fixing.  Added to that, one should be the observant with the time frame of work.