Credit cards and purchase orders are not mutually exclusive. Most organizations have preset spending thresholds above which you need prior permission. Once you have permission how you pay for it is a seperate matter.
Issuing credit cards to staff makes things more convenient for the staff member but can be fraught with potential problems (as we see). If people need to expense purchases on their own cards they are far more likely to think twice beforehand about making the purchase and will always make sure they retain proper receipts.
They are mutually exclusive if the organization has a coherant purchasing policy.
Credit cards are much cheaper to administer than going through the expense approval process which requires staff and overhead. They are more convenient, which means there are less internal controls associated with their administration.
The company I work for distributes credit cards to departments and certain employees who are advised to purchase insignificant corporate items with them rather than submitting expense claims and being reimbursed. Goods and services below a certain threshold are supposed to be purchased with a departmental credit card. Submitting an expense claim, having your manager approve the expense, having accounts payable cut you a cheque or administer an EFT are all expenses to the company.
Where I work, employees who have company credit cards need to reconcile the purchases to that card each month. The reconciliation is used to charge those purchases against that department's budget so the budget holder is responsible just like they would be with an expense claim.
It would certainly be much easier to purchase questionable items through a corporate credit card than expensing because there is a lot less control. If I make an expense claim, it goes to my manager for approval. But if a manager has a deparmental credit card, they are able to purchase items without anybody direcly approving of the expense. That being said, our credit card purchases are audited, so employees who had a habit of making questionable purchases would likely be caught. Audits are never comprehensive though, so organizations generally have purchasing limits on their corporate credit cards.