One is a SERVICE. Services sometimes have issues with profitability when scaling. You end up managing people and profit margins stay the same or decrease.

The other is a PRODUCT. Products generally scale better as the cost of product remains more or less the same (COGS).

Many people start consulting and build a product later.

You can also do a productized service which is a mix of both.

I think consulting is the perfect way to find the right SaaS opportunity. Consult with as many different companies as you can, find out the problems they have that make it difficult for them to achieve their goals.

Try and look out for the problems that are common between the various companies. Then you're already in a great position to validate and pre-sell a SaaS platform.

I've done both - founding a consulting firm, which is now 10 years old, and having co-founded a technology company (Healthcare Blocks - a PaaS for the healthcare industry). There are many, many ways in which these two business models are almost exactly opposite of one another:

The consulting firm has a handful of clients each year, with many contracts for six-figure dollar amounts. The technology company has many more customers, but the revenue per customer is lower.

The consulting firm has almost no recurring revenue (it's all project-based engagements that have a scope and an end date), whereas the technology company is almost all recurring revenue (subscription services) that is expected to go on indefinitely (there's no set end date at the beginning of the relationship).

The consulting firm was built largely on relationships, referrals, and word-of-mouth reputation, with almost zero spent on marketing and advertising. The technology company was built with on-line advertising, data-driven customer acquisition, paid referrals, channel partners, etc.

There are also differences in the flexibility afforded, the people you have to hire (or contract), and the capital required (I built the consulting firm with my own money, but raised some investor capital for the technology company).

As has already been said, you can start with one and look for opportunities to do the other. In fact, many consulting / services companies eventually try to build a product of some kind, to gain the stability of recurring and (somewhat) passive revenue. However, they don't always realize that these are two very different business models that have to be approached differently, so this kind of transformation fails more often than it succeeds (of course, more than half of startups fail anyway, so I suppose that's to be expected).

I have advised and helped dozens (maybe hundreds) of entrepreneurs in both business models. If you are interested, I would be happy to talk through some of these differences with you, and even learn more about your personality and preferences to help you determine which you might enjoy more. Let me know if that is of interest.