The practical differences cloud delivery makes to invoice processing are not about hosting. They are about who can act on an invoice, from where, and who can see its state without asking. Both of those attack elapsed time, which is where payables loses days, and neither shows up as a feature in a comparison table.
Approvals stop waiting for a desk
The most common cause of a late invoice is an approver travelling, on site or between meetings. When approval happens in a browser on a phone, that delay shrinks without any policy changing. This is the least glamorous benefit of cloud delivery and reliably the largest one in day-to-day operation.
One record everyone can see
Purchasing can see why an invoice is stuck without emailing payables. A site manager can confirm a delivery without a call. Most of the informal traffic around payables is people trying to establish one fact, and a shared record removes it. The cost is that access control becomes a decision you have to make explicitly.
What you now own deliberately
Who can see supplier bank details, who can approve on whose behalf, and how access is removed when somebody leaves. These had implicit answers when records lived in an office. Making them explicit is a small piece of work and a good use of a migration, since nobody revisits them afterwards.
Questions people ask about cloud invoice processing
Is cloud processing less secure?
Different rather than worse for most finance teams. The risks that actually materialise are access control and payment fraud, which are yours in any hosting model.
What if the service is unavailable?
Work waits, as it would with a local server outage. Ask for the actual uptime record rather than the target, and think about your month end.
Can we get our data back?
Ask what the export contains and test it in a trial. An export without the original documents is not a full record.