The wrongly framed question
The debate usually starts as "is cloud faster, or local?" In practice both architectures give similar performance in a single branch. The difference emerges when the system grows and when something goes wrong.
When the internet goes down
The right question to ask is this: when the connection drops, does the sale continue? A well-designed cloud POS keeps transactions locally and syncs when the connection returns. Sales don't stop, orders aren't lost.
It matters to see this in the contract. The "cloud" label alone does not guarantee offline resilience.
Who holds the data?
In a local setup the data is on your device: control is yours, and so is the backup responsibility. In a device failure, theft or fire scenario, do you have a recovery plan?
In the cloud the data is on the provider's infrastructure: backup and access are their responsibility, but your export right must be clear in the contract. The answer to "is the data mine and can I get it whenever I want?" must be in writing.
Before the question of cloud or local: can I get my data on the day I want?
The cost of the second branch
The difference shows most here. In a local setup each branch comes with its own server, its own installation and its own updates; as the number of branches grows, the management burden grows linearly.
In the cloud a new branch is an account definition: the menu and price template is copied and it opens within minutes. Setting rules from the center is only practical in this architecture too.