On the smaller boats, the power tilt and trim or manual tilt mechanism is a primary way to control the pitch attitude of the boat. Tilt in to make the bow go down, tilt out to make it go up — those are the basics. You want your hull running through the water at a comfortable and efficient angle for the conditions you are encountering. In smooth water, you can find the most efficient tilt angle by setting the engine to cruise power with the engine trimmed all the way in, and then gradually trimming out while monitoring your speed using a GPS. At some point, your speed will max out and begin dropping and/or your boat will begin to cavitate and porpoise. That means you just exceeded the best angle.
Larger boats with large outboard or inboard/outboard (sterndrive) engines are often also equipped with hydraulic trim tabs attached to the hull. Now there are two ways to control the attitude of the boat: you can deflect the trim tabs down, pushing the stern up and the bow down, or you can tilt the engine down, which will tend to do the same thing. Which one to do?
Use the Trim Tabs or the Engine Trim?
The answer will depend on the conditions and on the particular boat and how it is loaded, but the general idea does not change: Decide on the attitude at which the boat should plane over the water, and use the trim tabs as little as possible in order to achieve that angle. If you want the bow down, try trimming the engine in a little bit. You will not increase the drag of the engine very much by running it with the thrust directed slightly downward, and getting the boat to ride at a better attitude may increase speed for a given throttle setting.
If you achieved the same result using trim tabs, you would have to create some drag by deflecting the tabs down into the flow of water coming off the aft end of the hull. In most cases, that additional drag will be greater than any created by trimming the engine in a bit.
On boats with more than one engine, the engines can be trimmed to slightly different angles to adjust the left and right (roll) attitude of the boat. Trim the starboard engine out and the port engine in to cause the boat to roll slightly to port. If you have more weight on the starboard side, causing the boat to list a bit in that direction while cruising, you can level the boat back out somewhat by using differential engine trim, and if that is not enough, use the trim tabs to finish the job.
Trim tabs are very effective, and can overcome large weight imbalances, but they do so at a high price in drag, and any efficiency which may be gained by improving the cruising attitude of the boat will be at least partially offset by that loss. Hydraulic power tilt and trim on your engine is usually the more efficient way to adjust your boat's pitch attitude because small changes can be made without much effect on engine drag or the effective use of thrust, and those changes can have large effects on the speed, comfort and efficiency with which the boat planes across the water.