Way back in 2001, Topps had a terrific idea. They started a new series, Topps Heritage, using designs from classic Topps cards of the past. That same year, Upper Deck had the same idea, to put out a series of cards based on classic Topps designs.
2001 Upper Deck Vintage
2002 Upper Deck Vintage
2003 Upper Deck Vintage
I think that Upper Deck came the closest to copying the original Topps set in this year.
My extensive training in copyright law (I read a couple of Wikipedia articles) suggests to me that Topps, which has clearly copyrighted their cards, let their copyright lapse. If I'm understanding this correctly, prior to 1976, a copyright was granted for 28 years, with one 28 year extension. All these Upper Deck sets appeared more than 28 years after the Topps sets they were based on. I don't remember hearing about any flap between Topps and Upper Deck back then.
2004 Upper Deck Vintage