The problem with paracetamol is it can be very dangerous if too many are taken - and it is in such a lot of products, so it is important to read the label.
Some people can't take aspirin - asthma sufferers for example.
Some people can't take paracetamol - alcoholics and those with liver problems.
It really is down to personal circumstances and choice.
If there is no reason why either can't be taken, I would prefer paracetamol where there is a temperature, and aspirin (or ibuprofen) for pain without temperature.
aspirin = both of above, but its also anti-inflamitory which is ideal for sore throats, earache, inflamation etc but always read the label. aspirin isnt suitable for under 16yrs, it may cause upst stomachs.not suitable for asthmatics or those who have stomach ulcers, however i find soluble aspirin wonderful for sore throats (gargle then swallow)