Bordeaux would be geographically closer, but Lyon more interesting, given your stated interests.
Background: I lived in Lyon for a few years, have visited several times before and since then for work or leisure (or doctor's appointments) and I've only visited Bordeaux twice. So, I know much more about Lyon than Bordeaux.
That said, it's not even close. Everything you mentioned as an interest is more prevalent and diverse in the much larger Lyon area than Bordeaux. The key thing I found interesting in Bordeaux was how the wine business of that area grew due to Dutch and British influence, and how it differs (profoundly) from the wine growing, making, and marketing of Bourgogne, with which I am far more familiar.
Lyon is not a wine growing area. But you can sample practically any French wine (and some from other nations) there. It's been said that there are three rivers flowing through Lyon: the Rhône (from the mountains of Switzerland), The Saône (from the Vosges upland of eastern France) and Beaujolais, the wine made just north of Lyon.
You can't go wrong with either place, but if I had 5 to 7 days to visit either Bordeaux or Lyon, I wouldn't hesitate to spend it in Lyon.
Edit: A small anecdote to illustrate the differences between the two. The leaders of Bordeaux commissioned an important bronze sculpture to be crafted by Frédéric Auguste Bartholdi, the sculptor of many monumental works of art including the Statue of Liberty and the massive Lion of Belfort. The leaders of Bordeaux started and stopped the project a few times, concerned at the cost, and eventually sold it to Lyon. It was completed and became yet another one of the unmissable highlights of the city. It's been recently restored and has long graced La Place des Terraux in Lyon, a UNESCO world heritage site, where each December Lyon's heavily-attended Fête des Lumières is anchored, with creative lighting projected onto the building fronts surrounding the place.