It depends. While both can be used to categorize keywords, their usage is quite different.
Tags are used to classify keywords, and make it easy to sort and filter. One keyword can have an unlimited amount of tags attached to it, and they can be used in conjunction when filtering.
Keyword groups are used to track different sets of search engines or comparison URLs. If you want to track one group of keywords in a set of search engines and track another in a different set of search engines, the best way to achieve this is with keyword groups. Putting the same keyword into multiple keyword groups will cost you multiple keyword credits, and is not recommended if the search engines and comparison URL's are the same.