Are there any disadvantages to using threat intelligence services rather than threat intelligence products?

I think it comes down to the fact that, if you don’t have internal expertise and trained staff, then threat intelligence services are great.

But if you have the people, then they can use the threat intelligence products to often do a better job than the then threat intelligence managed service providers.

Outsourcing to a third party threat intelligence service can be extremely useful and can free up internal resources to be used for ore pressing needs.  On the downside, there tends to be a lack of intimate knowledge from a third party; in theory, no one should know your environment, needs and quirks, as well as your own internal staff, who probably helped build out your environment.  It's like being a homeowner who knows every creaky floorboard and every leaky faucet in the house, vs. a handyman who has no real bond with your home.

 There is an advantage in using a 3rd party threat intelligence service where you outsource this function vs having a product that you manage and maintain, especially if you don't have the manpower or skills required.
In my opinion its best to use threat intelligence product that ingest various threat intelligence sources so its more comprehensive.