Private lessons have several advantages.
One of them is to have an experienced Tango dancer giving you corrections that are particular to your dance.
Another, is dancing with an expert with many years of experience.
And there are many more.
In group classes you learn the social aspects of Tango, to move among other couples, practice useful exercises, make friends and start to integrate yourself in the society of Tango.
However, not everybody has the same goals regarding Tango, and this is something to keep in mind about group classes.