That depends on the type of suggestion the autocomplete options are suggesting.

Take Chrome for example. If I type in a term and it is suggesting a search term, which will take me to the search results page, it looks like this:

But if the suggestion is for an actual URL / resource, which will take me to that URL / resource, then it looks like this:

There is a clear differentiation between items that are a search suggestion and those that are a resource. It would waste my time to take me to the search page when I have accepted an item suggestion. At the same time, then only logical place to take me for a search suggestion is the search results page.

So, as long as it is clear what type of suggestion you are making, you should display the most relevant type of page for the type of item being suggested.

That depends on the type of suggestion the autocomplete options are suggesting.

Take Chrome for example. If I type in a term and it is suggesting a search term, which will take me to the search results page, it looks like this:

But if the suggestion is for an actual URL / resource, which will take me to that URL / resource, then it looks like this:

There is a clear differentiation between items that are a search suggestion and those that are a resource. It would waste my time to take me to the search page when I have accepted an item suggestion. At the same time, then only logical place to take me for a search suggestion is the search results page.

So, as long as it is clear what type of suggestion you are making, you should display the most relevant type of page for the type of item being suggested.

As a side note, many services choose to simplify things and only show a search suggestion. That way no matter what you search for, you will always be taken to the search page. Amazon is a good example of this.