It will depend on the placement of perhaps mainly the light pieces and the queens. Attacking the enemy d-pawn is definitely an option. Over-protecting your own d-pawn is also an option. Placing a knight on the (for white) e5-forepost is an option.
In general, it is a good idea to have a knight that is ready to grab the enemy d-pawn when given a chance. The reason is because the enemy will try to build pressure on your d-pawn by placing the queen (as black) on b6 or f6. Then, as white, you are ready for e.g. Nc3xd5 hitting the queen.
You can consider placing a bishop (as white) on the h1-a8 diagonal to pressure the enemy d-pawn. Note that when you play Nf3-e5, you lose a defender of your d4-pawn and black can build up on d4.
With the heavy pieces, you should probably invade on the c-file (since the enemy has castled kingside and the c-file is further away from the enemy king than the e-file). You can try to use the c5-forepost to weaken the enemy queenside and invade with a rook on c7 or c6 (also push b2-b4-b5). Then, later, you can place a knight on c6 (given that black has done b7-b6 and made c6 weak).