The forest comparison is not accidental. Gaudí designed the columns to branch at different heights and carry the weight of the roofs and vaults down to the foundations, which let him do without the flying buttresses of Gothic cathedrals. The Basilica's own architectural documentation calls these columns "structural trees".
If you can choose your entry time, think about the light. Morning sun comes in from the east, through the cooler blue and green glass on the Nativity side. Later in the day the western Passion side glows with reds and oranges. The effect also changes a great deal with the season and the weather.