My favorite playstyle? Hmmm...... MY OWN!
Well, to be more accurate, I think my play style comes close to the balanced play style, but I don't really care about all those different words for the different styles.
What's most important for me, is to have a good synergy and variation on my teams, so my Pokémon are able to cover each others weaknesses, and to utilize their strengths in the different situations.
One of my own rules when building a team is to make sure, that no more than 2 Pokémon on my team has the same weakness. For example, 3 Pokémon which has a weakness to Ice, is not a possibility for me, as it gives a bad synergy.
I also make sure to always have at least 1 Physical Wall, 1 Special Wall, 1 Physical Sweeper and 1 Special Sweeper to ensure a good balance between offense and defense.
Just like a football team, you have to both use defensive players and offensive players, so you can deal out damage, and take damage too.