There appears to be a level of confusion about what an allowance is and what a reimbursement is. People sometimes don’t make a distinction or get it wrong entirely and sometimes this is even propagated by the company themselves. This is generally because the business will benefit from your confusion by not having to cover some of your business-costs. So, in essence, an allowance is an amount of money that is regularly given to you by your employer to cover any out-of-pocket expenses you incur in your job. This might be ostensibly for transport, or for a uniform etc. This regular stipend might be spread over the year or given in one lump sum.
The crucial thing here is that it counts towards your total taxable income. Therefore, if you are paid $50,000 a year with $5,000 allowance, your total taxable income is $55,000. However, while it adds to your total taxable income, you can still claim a deduction based on your business-expenses.
A reimbursement though is something that is completely different. A reimbursement is generally used for one-off or irregular expenses you might incur. For example, if you have to travel to meet a client for an out-of-town meeting. Generally you would pay for this amount up front (or if you know the amount beforehand you can request the money first) and then the company would give it back out of petty cash.
This type of transaction is a business expense only however and never really comes out of your pocket. For this reason, it is a business expense, covered by the business and not you. The money you receive for this is not part of your total taxable income. For example, you are paid $50,000 a year but you are reimbursed for $3,000 of expenses over the course of the year. You still have a total taxable income of $50,000. However, crucially, since it a business expense and the money doesn’t come out of your own pocket you cannot deduct the costs from you taxable income.
The bottom line is that if it is on a PAYG summary, it is an allowance and you can claim deductions for expenses. As for which one is preferable: if you spend more on your expenses than your allowance then being reimbursed by the company would be better. If your allowance is more than your business-related expenses then it will be a good idea to stick to the allowance.