If you are staying in an inside cabin anyway, I can't see much difference there. We have never sailed on Sun, but we have stayed on the fourth deck on a different ship. You will have less motion on the lower decks, but you may hear more engine noise on the lower decks if you are toward the stern of the ship. There may even be an advantage because you will be closer to the restaurant, and the shopping on board ship.
Deck 4 is the main traffic area for all guests to embark and disembark the ship in nearly every port. That means that over 2,000 people will be passing your cabin door at least twice a day. When they must line up to get off the ship, they will be standing outside your cabin door with noisy children, many complaining in very loud voices about having to wait in line.
Noisy hydraulic and high pressure water lines are located in some areas of the lower decks. They tend to be noisy at inconvenient hours. The crew cannot stop the noise.
Deck 4 forward puts you hear the anchor chains and bow thrusters. These can be very loud during arrival and departure.
Deck 4 midships has the hydraulic shell doors (very noisy opening and closing) and the tender platforms. If the ship is tendering, ther will be lots of noise and shouting, and tender boats occasionally slamming into the hull outside your cabin.
Deck 4 aft puts you near engine room, workshops, crew bar, prep kitchens, and loading areas. These facilities tend to be in operation 24 hours a day.
The tradeoff to this possible inconvenience is a lower price. Only you can judge if the tradeoff is worth it.
We have stayed on the fourth deck twice, although not on this ship. The only noise we ever heard was the anchor chain, and that hardly bothered us at all. This was on one cruise, when we stayed pretty close to the bow of the ship. Other than that, we heard very little noise at all. For me, I'm satisfied on the lower decks for the difference in price. After all, we are on a fixed income, and if we can sail for half the price of the upper decks, that means we can sail twice as often.
We got off the Sun on Oct 1 and the main passenger embarkation deck is Deck 5. Tenders were from Deck 3. Our cabin was 4030 (Outside mid-ship) and it was very quiet and smooth. So if you're in the same vicinity it should be fine. We only anchored once and heard nothing. BTW, a lower deck generally means less motion than a higher deck, it's just farther to the pool and buffet. We did not find the elevators on this ship to be as busy as on others we sailed.
Now when we were on the Monarch of the Seas in March we did hear the anchors one morning as we were forward on Deck 3. Note that Deck 4 on the Sun is not Deck 4 on the Monarch etc. Consult the brochures as each ship is different.
Anyways enjoy the Sun - it was our first time on NCL and we really enjoyed it.