This gets debated as a technology question and it is not one. Both options do the same things. What differs is who carries which risk, and that is a business decision.
Answer these five and the choice usually makes itself.
1. Does a regulator or a client contract say where the data lives?
If yes, the answer is already written and the other four questions are academic. If no, do not invent the constraint. A surprising number of on-premise deployments exist because somebody assumed a rule that nobody had actually read.
2. What happens to your business if the internet drops for four hours?
On-premise keeps internal extensions working through an outage. Cloud does not: no connection, no calls.
For most offices this is a nuisance. For a clinic taking appointments, a dispatcher coordinating drivers, or a site office in an area with genuinely poor connectivity, it is the whole argument. Be honest about which you are, and about how often your connection actually fails, because the answer is usually less often than the memory of the last outage suggests.
3. How many sites do you have, and will that number change?
Cloud gets easier with each additional site. On-premise gets harder with each one, because every site is either another box or a dependency on a link to head office.
If you expect to open somewhere new in the next two years, that alone usually settles it.
4. Who patches it?
Both need updating. The difference is whose calendar it appears in.
With cloud that is the provider's problem. With on-premise it is yours, or it is your partner's under a contract you actually signed. What it must not be is nobody's, which is the most common outcome and the reason so many on-premise systems are three versions behind and quietly exposed.
5. Which cost shape suits you?
On-premise is capital: buy the hardware, own it, replace it in five years. Cloud is operational: no upfront purchase, a monthly bill that never ends.
Neither is cheaper in the abstract. Which is cheaper for you depends on your cost of capital and how long you keep equipment, and that is a finance question rather than an IT one. Ask your accountant, not your integrator.
The hybrid, and when it is real
Hybrid gets offered a lot and is genuinely right occasionally: head office on-premise for the regulated part, branches on cloud. It is also the answer people reach for when they cannot decide, and then they run two systems and pay for both.
If you cannot say in one sentence which part is on-premise and why, you do not want a hybrid. You want to answer question one properly.
The short version
If you are unsure, it is cloud. On-premise is the right answer when something specific makes it right, not as a default and not as a comfort.