Both trailers focus on the relationship and the inevitable showdown between Violet Crawley (Dame Maggie Smith) and Cora Crawley's mother, who will be played by Shirley MacLaine.
Earlier this month, MacLaine teased that there will be "a little sparring" between the pair on screen.
She shared: "We do a little sparring but it's more sophisticated and adult.
"My character is really trying to explain to her that you really must grow up and out of this addiction to tradition because this is what got you into the World War."
MacLaine described her character as smart, sensitive and extremely outspoken.
Creator Julian Fellowes also previously said that the third season's themes will be about financial woes and the Irish Troubles.
Season three of Downton Abbey will air in the autumn on ITV1 in the UK, followed by a 2013 premiere in the US on January 6.