This is one of the more interesting questions asked of me, SaaS or on-premise, which is better? This is one of those classic consultant questions with a classic consultant answer..."it depends."
Every business is unique and there are several factors to consider when trying to decide "which is better" for you. But there are a few factors that seem to really separate the field, 1. Money , and 2. Management. Obviously there are more factors to consider, but these two usually help to really put you on one side of the line or the other to start out.
This factor basically boils down to your access to capital for spending on a new system. If you have the money up front to spend on a major system, then access to on-premise solutions isn't out of your reach because you have the money to spend up front. One single investment in the system and then you can start building it and putting it in place. However, not everyone is budgeted for a major capital expense. In that case, you will find many businesses who opt for the SaaS model because it allows them to buy the system as cash flow in operations allows them to spend.
This factor is meant to separate those who are capable and have the resources to manage a major system on their own from those who don't have the technical resources to keep a major system running. This can be a big deal for some businesses. You are about to take on the responsibility of acquiring and building, and maintaining a major system on-premise. This means when it goes down, you are responsible for getting it back up. This means that when you need to upgrade the OS with security patches on Tuesdays, you are responsible. Not everyone has these kind of resources. There are plenty of people who just want the system to provide the business benefit and can't afford the people to maintain a major system. If you can afford the onsite resources and are willing to take up those responsibilities, on-premise may be for you. If you are interested in having experts maintain and manage the system and just want the business benefits...you are probably looking for SaaS.
This is just a starting point for deciding what you want. I have plenty of examples where companies that have plenty of money and IT resources opt for SaaS for other reasons. And, as surprising as it is to me, there are companies who really can't afford the IT resources, end up buying a budget on-premise system to maintain for themselves.
Please share the simple factors that you find are clear markers for decided on-premise vs. SaaS. Drop me a note at firstname.lastname@example.org.