An executor's job is to carry out the wishes of the deceased as laid out in the will. The executor is also responsible to sort out tax issues, settle debts, bequests, etc. An executor is someone trusted implicitly to carry out those instructions.
To be honest, I wouldn't relish the idea of being part of an executor "committee". There's too many "cooks in the kitchen" IMO with 4 executors, and the scope for disagreement/conflict is too great.
My father had a bank named as his executor. They were very efficient, and certainly there was no issue of complicated family dynamics. However, the bank charged alot of money to perform those duties. And it meant that his heirs received less as a result.
My grandfather appointed his daughter as executor. She liased closely with the solicitor's firm that drafted the will. Not sure it was cheaper than using the bank though. The daughter took an executor's fee (which you are usually entitled to if the estate is complicated and time consuming to settle), and there were significant legal fees.
It's an important decision, and a tough call.