It is possible to do both in one day, especially in spring or summer, when the days are a bit longer. But it is not a good idea, or a good option, to use your words. You should keep in mind that the transfer from the centre of Ghent to the centre of Bruges will take one hour (or more), by train or by private car. The main train station in Ghent (Sint Pieters) is a 25 minutes walk from the city centre or 10 to 15 minutes by public transport. In Bruges however, the train station is next to the centre.
I am bit afraid that by trying to see both I end up running the whole
day and not enjoying neither one.
That's exactly what will happen when you try to fit both cities in one day. Thus, if you can, spend one day in each city. Or pick one. Which one is difficult to tell. It's like Android or iOS, Burgundy or Bordeaux, red or blue, etc. However, the following sentence makes it a bit clearer:
I just want to walk around, get the feeling of the city, try local
food and maybe visit one or other important place. I am looking for a
Go to Gent. Bruges is indeed a beautiful place, but crowded by tourists. It's a kind of Disneyland. Ghent is beautiful as well, but it is real and authentic. Even in the city centre you will meet real people and not only tourists.