I would say: both ! As a wine and tourisme expert, don’t ever think of spending only one day in this beautiful region, but at least 5 days: one in Medoc, one in Bordeaux, one in Saint Emilion, one in Pessac/Graves and the last one in Arcachon Bay or Sauternes area.
More seriously, knowing your agenda is very tight and that you have the only possibility to spend one day outside Bordeaux, then it all depends on how much you are « into » wine and what you expect from the vineyards.
If your main reason is to visit wine chateaux and taste renowned Bordeaux wines, then either the Médoc or Saint-Emilion will definitely meet your expectations. Bordeaux’s and even world’s finest wines are produced in these two regions. So you won’t get wrong in choosing one of these areas.
If discovering wine and learning more on local grape varieties are your main objectives, then figure out which region makes the wines you most enjoy. It could be a particular château, estate or a particular style of blending of the 3 main red grape varieties that varies according to the area: firm, structured Cabernet Sauvignon-based blends are found in the Médoc, that has had a long history of making very full-bodied red wines with high tannins, low acidity, and medium to high alcohol levels: in other words, the classic Bordeaux blend. Saint-Émilion the softness and light sweetness of Cabernet Franc and especially Merlot bear a distinctive magic all their own. With time, the best wines mature to a silky complexity.
The type of landscape and sceneries vary also from one region to the other. In the Médoc, you’ll admire gorgeous chateaux, really grand and impressive buildings, large and outstanding wine producers such as Margaux, Lafite, Mouton Rothschild, Cos d’Estournel, … Villages are small, quite plain. In Saint Emilon, the wine producers are smaller, less impressive but very elegant. Villages though are more picturesque.
Medoc for wine chateaux, Saint Emilion for its exquisite village
That is why, if wine is not the primary reason for spending a day among the vines, you might want to go to Saint-Emilion. Here the wines are magnificent, as good as those in the Médoc, but what makes this area different is the beauty of the landscape and the village of Saint-Emilion itself, inscribed on the UNESCO list of World Heritage Sites in 1999 that is partly carved from the rock that surrounds it.
You can spend your whole day just strolling the streets and enjoying the town of Saint-Emilion without ever visiting to a single wine château located around the villages. Even though you should! At least to have lunch in one of the few estates that serve stylish and delicious meals in unique settings overlooking their vineyards. Make sure you have a guided tour of the village including the Monolithic church, the Cloister and La Tour du Roy.
There are almost 800 châteaux in and around St-Emilion. Easy to get headaches when choosing ones! Again if wine is not your priority, rely on your instinct and, above all, your travel guide !
Medoc chateaux where known not to encourage visitors to step in for wine tasting. Historically, their tasting rooms were mostly open to really serious buyers or highly specialized groups. But it has dramatically changed for the last 5 years, and now private guides generally can get you in, if you make appointment ideally with a reliable agency some days in advance. You’ll be driven on the « route des chateaux » passing well-known and many classified growth châteaux like Mouton-Rothschild, Latour, Palmer or Pichon-Longuneville. Pause at a few photo-worthy places. But, make sure you are with a small group if you were to have a private lunch in one of them. Those chateaux don’t open for individuals only. Ask your wine agency to organize it for you.
Whatever you choose, make sure you have a guide and/or a driver so that you can fully enjoy your day tasting wine and appreciating the very minute you spend on the wine roads. Unless you are a “wine geek”, don’t go over 2 wine tastings per day. Make sure they are totally different with different techniques and blending so that you get more familiar with the wine process and styles.
You’ll come back anyway to visit the region you missed !
Visit Sauternes, for example, which is gold to the Bordeaux vineyards, a sweet, syrupy AOC, classified in 1855 with the prestigious Château d’Yquem as the only Superior First Growth.