Aggressive vs defensive is not always black and white. It happens in the matter of degrees. Almost all characters have some defensive capabilities and some offensive capabilities. Which kind of character they are is determined by how many of options they have for aggression or defense, as well as the quality of these options.
Defensive options are basically tools that you can use to zone and control the stage. Zoning someone means that you are limiting their options or forcing them to commit to a certain option. When you're approaching sheik and she's charging needles, you are forced to periodically sheild while you're running at her to avoid damage. Or when Duck Hunt places a can on the stage and you're forced to jump over it or shield it. Or when you're approaching Rosalina and luma is acting as a literal wall to your attacks. Zoning has to do with hindering your opponent when they're trying to approach you. Most defensive tools are/have long range, disjointed hitboxes, safe on shield, projectiles, lingering hitboxes, high priority, etc
Aggressive options are defined by zone breakers, and moves that prop your opponent into a disadvantageous spot. Zone breakers are attacks that are faster than you can react to, and that have decent enough knockback to give you stage control when you land them. Examples of zone breakers are most characters' dash attack and nair. And then moves that allow you to put your opponent into disadvantageous positions that allow you to keep putting pressure and aggression on your oppoenent. Moves that lead into air juggles, combos or edgeguarding fall into this category.
What kind of character is Ness? I would consider him an aggressive character. He lacks enough quality defensive tools to be played successfully in that way all the time. The only zoning capabilities he has is pk fire, fair, and pk Thunder. Fair is great against almost all aerial approaches, but is pretty poor at stopping or inhibiting ground approaches since it doesn't have enough range to be safe on shield, unless you retreat with it and give up stage control. Pk fire lacks both the range and speed to be used as a safe spacing tool. If anyone just runs in and shield you you'll get punished. You can typically react to it since it's so slow. Pk fire is a punishing tool, used for capturing landings, and spotdodges, as well as other things. It is not a good spacing tool in the majority of situations.
However for aggression ness has quite a few options. For zone breakers he has a wonderful dash attack and fair. Dash attack not only has wonderful range and disjointed hitboxes, but props them up in the air for a juggle. Nair also has amazing speed, and has enough knockback to give you a lot of control over the stage. If you approach and land a rising fair, you can lead to more fairs. Approaching with a dash grab leads to either a dthrow with combos, an fthrow with edgeguarding, or an uuthrow to juggle. Running up and short hot nairing or fairing is a great way to stop someone if they rely heavily on aerial defensive options.
I would consider ness to be a rush down character simply because he has the tools to break through zones, as well as the tools that put his opponents in bad positions.
What makes Ness unique from other rush down characters? Well unlike sheik, or falcon, he has very low mobility. A lot of aggressive characters rely on being
Mobile, since it makes it significantly easier to break through zoning. Ness has a pretty terrible dash speed and Max air speed. What does he gain in compensation for this? He has a pretty huge reward for landing hits. His damage per hit is very high, and he has his wonderful fair combos which heavily inflates his reward for landing a grab. What makes Ness different from other characters that are forced to approach, have poor mobility, and great reward? These kinds if characters would be Luigi, Doc, Ike, and the Heavies. He is much smaller than all of them. He is lighter than the heavies. And he has a much easier time getting out of juggles compared to the rest of the characters in his class. Ness's wonderful aerial acceleration and deceleration means that he can often wiggle around and past characters that are trying to juggle him. Ness's size and floatiness also make him difficult to combo.
However, I would say that Ness's most unique characteristic is his Pk thunder. There is nothing else in the game like it. No other projectile is designed to be so medicore and poor in neutral, yet spectacular in advantageous positions. No other projectile is as controllable and precise as pk Thunder, while lasting a long time. Pk Thunder also bounces them up, leading them to another bad position and often times another pk Thunder. And no other projectile has the threat of leading into one of the strongest KO moves in the game if a player is too preoccupied with dodging the projectile.