You need to separate inputs and outputs.
Historically there have been (to keep it simple) two inputs to Google's search results, these being structured and unstructured data.
Once the input is there, it can be used in a number of ways by Google. Some ways may affect ranking. Other ways may affect snippets. These are outputs. Structured inputs have been shown to have beneficial effects on rich snippets, making the effort of structuring the data worthwhile.
With the addition of this new tool, Google has added an input. The input is roughly equivalent to structured data, but it's not as precise. If you're capable of marking up your content with schema.org markup, then IMO you should continue to do so. It's far more accurate. The highlighter tool may be better if you're not capable of marking up your content, e.g. because you find it too technically difficult or because you use a CMS that does not allow you to edit the code at the level required.
The results (i.e. outputs) of using the data highlighter tool should be roughly equivalent to using schema.org markup - you're modifying the inputs when using the tool. Thus, use of the tool may give similar rich snippets to those available using schema.org markup at present.
The reason I ask is that I run an event-listing site that might benefit from this tool. But I'm anxious about how much information Google will give away in their search results page. I don't want my potential visitors to get all the information they need from the SERPs, and therefore not have any reason to visit my site.
Typical event results can be seen at
You should decide if such listings would be beneficial to you. In my experience, they normally are.