Vander Els Partners
Either can work. What matters more is who Google bills, and whether the agency's fee rises when your spend does. Those two details decide whether the agency has a reason to spend your money well or just a reason to spend it.
Who gets the invoice
If Google bills your card, the media invoice sits in your own account. You can read it any time, see exactly what was spent and on what, and you never need to ask anyone for a screenshot. If the agency pays Google and bills you back, you are trusting a number on someone else's invoice, and the agency is holding your ad account, which becomes a problem the day you leave.
Whatever the arrangement, the ad account should be in your name. Not migrated to you later. Yours from the first day.
Percentage of spend
Some agencies charge a percentage of what you spend on ads. It is common and it is a conflict. An agency paid that way earns more when you spend more, whether or not the extra spend produced a job. The pressure is always upward, and in a market that cannot absorb the money, that pressure costs you.
A flat fee removes it. The agency then has no financial reason to push money into a market that cannot use it, and every reason to spend the least that still works. Ask any agency you are talking to how the fee moves when the spend moves. The answer tells you what they will optimise for.
Inside or on top
Inside the retainer means one number a month, and the split between work and media is set before you sign, based on what your market costs. It is simpler to budget and it removes the surprise of a media invoice arriving beside the fee. The risk is that a bad agency starves the media to protect its margin, so the split has to be written down and visible.
On top means the fee and the media are separate lines. It is more transparent by default, and it is easier to compare agencies on fee alone. The risk is that the media number creeps, month after month, because nobody has a reason to hold it.
Both can be honest. Both can be abused. The written split and the flat fee are what make either one safe.
The short version
Insist on three things whichever way it is structured: Google bills your card, the account is in your name, and the fee is not a percentage of spend. With those in place, inside or on top is a bookkeeping preference. Without them, it does not matter which you pick.