Different water profiles can change the taste of your beer. Especially when you brew a beer with - as you say - "nothing [...] complex with tastes". When there is no big hop aroma or lots of alcohol in the beer, the subtle influence of the water shines through.
The water chemistry can accent the hop bitterness, and it can also support the malt flavours.
Even though the "breweries" aren't so far apart from each other, they can have complete different water. Even within a city the water can be from different sources. When I lived in Heidelberg, Germany, the water in the old town of the city was known for its soft water, that came from the mountains behind the castle. The rest of the city had harder water from a different source.
Try to get a water report for both breweries or even better buy a water testing kit like the iDip or the BrewLab from LaMotte. You need to know how your water is before you change it. Or start with distilled or RO water and add the salts that match the beer style.
Have a look at the Bru'n Water Website: it is a great resource for information on water and offers a water calculator, to find out how to manipulate your water for different beer styles.