You've discovered one of the dark secrets about scoring high, young padawan -some characters are indeed better for that than others- but there are others.
In my experience the knowledge of spawns is the biggest factor. I often outscore PUGs with better weapons and consumables not because I do extraordinary things from a technical point of view or headshot all my enemies, but simply because 9 times on 10 I know where the enemies are going to spawn (based on the spawns locations and the positions of my teammates), so I'm almost always the first to reach the enemies. Each map, given its size and the locations of spawns, has its own rythm. When you have played this game a lot, you almost "feel" where the enemies are and when they are coming in your back / flank and so when you need to reposition. That's why -for now- you can't match the score of the most experienced players ; they simply know this rythm better than you do.
Ex on White : given how players position at the beginning of the waves, enemies often spawn at the bottom of the map, near the ammo crate. Then, when this spawn is destroyed, the second one often occurs on the ramp in your back (where people camp in solos), unless a teammate is positioned here (enemies can't spawn too close to a player, most of the time*). If that's the case, go check the extraction zone : enemies are probably here. Once you're familiar with this mental exercise -predicting spawns based on their predetermined locations on each map and on the positions of your teammates-, then your score starts to seriously increase.
An other tip to score high is to know, for each faction, which enemies have the best ratio points awarded / time needed to kill them, and to focus on them. Of course, it depends on the character and weapon you're using, but, to simplify : ignore bosses and focus on mooks / sub-bosses. For instance, killing a platinum Phantom will credit you 1760 points, while, with certain weapons like the Venom, you only need 2-3 seconds to kill them. Killing an Atlas will of course give you more points, but not so much : only 2700, while you'll probably need more than 30 seconds to kill it. Following this strategy has also the advantage of making games faster.
The last factor I can point out is that hosting gives a significant advantage regarding the score, not only with vanguards. It's pretty obvious, but everything works better on host.
However, you must be aware that the score isn't always a perfect measure of the players' relative skills. I mean for example that, when an enemy is killed by a combo of powers, the primer gets the points for the kill. So characters who are good primers (like a Paladin spamming Snap Freeze everywhere, or a human adept putting a Singularity in every choke point) get their score "inflated" simply because of this score system. People playing this type of characters are often going to topscore, and often outscore players of higher skills. This also applies, notably, for characters whom powers have a big area of damage and a massive damage boost against armors, like kits with Flamer or Inferno grenades.
*Besides pyros aka super cheaters