The pump is what drives the filtration system and must be correctly sized to the filter as well as the pool volume. The first rule of thumb is 0.5 horse power (hp) per return jet in the pool. So for an average 60,000 lt pool with 3 return jets you need a 1.5hp pump.
The flow rate of the pump is critical for proper circulation. The pool is required to be turned over (i.e. the whole volume filtered once through the system) twice a day in Summer and once a day in Winter. Ideal is a 3 to 4 hour turn over rate. So in less than 4 hours your filter pump combination should be able to filter the whole pool volume once.
To work out the flow rate required simply divide your pool volume by 4. For a 60,000lt pool you need a pump with a flow rate between 15,000 (4 hours)and 20, 000 (3 hours) lt per hour. Then match up a suitable filter with that designed flow rate.
Yes bigger is better, but if you upgrade the pump then you need to up grade the filter as well. Not all pumps are the same by the way. You can have 3 different 1.0 hp pumps and they will have different flow rates, depending on pump design. You can also pay 3 different prices yet they have the same warranty. Keep it as simple as "you get what you pay for".
TIP: Look for pumps with a 3 year warranty, it's worth the extra money to buy a better quality pump.