Really, Let's compare, or heck, let's use Bulbapedia!
And Lance's:
But hey, don't take Bulba's word for it. Let's really get into the nitty gritty, shall we, and compare and contrast their overall usefulness and see whether or not Lance truly did more in Rocket HQ than Cynthia did in the "entirety" of Platinum.
Right away, I can definitely see that's a lie, since Cynthia has made a gazillion appearance to help the player throughout their journey, while Lance (and I verified this by watching several LP vids of Rocket Hideout) has made a grand total of roughly around 4 appearances in the Rocket Hideout. So, that being said, let's get into the appearances and what they actually mean in context:
Lance:
Appearance 1: You find the Rocket HQ with him. He said he'll explore it, and does so, with you following behind him.
Appearance 2: You meet Lance a second time after you go down a floor, where he heals your Pokemon so you can continue.
Appearance 3: He tells you something that you basically already know, anyway. Team Rocket Grunts have the passwords, you need to find it.
Appearance 4: He helps you in a battle against TR, and then disables the machine with you, and he thanks you for your work, and he leaves.
Cynthia: (and we're talking only Distortion World here)
Appearance 1 & 2: Gives you some background on Giratina, and informs you that if nothing is done, the actual world would be destroyed along with the Distortion World. Same for her second appearance after you actually travel into the distortion world.
Appearance 3: Basically informs the player that the Distortion World is a maze (something you knew mostly, already) and that you need to reach the bottom to see Giratina.
Appearance 4: Gives you more background about Giratina, says that you'll have to split up with her and she'll meet up with you.
Appearances 5: Either tells you that the specific area you're in (or maybe the Distortion World itself) is a puzzle (no muk) and that you'd need to solve it to keep moving. She then tells you to go to Uxie/Mesprit/Azelf as they'll help guide you through said puzzle.
Appearance 6: Informs you that while the Lake Trio can hold their own against Dialga and Palkia, that they may not fare against Giratina, and thus that's why they might have gone home.
Appearance 7 & 8: You meet her and she tells Cyrus basically to psyduck off ("Why do you seek to change the world? If you hate our world, you should just go off somewhere alone. Find somewhere where you can live without seeing others").
Her "8th appearance" is basically her telling you that what Cyrus says is bullmuk and you shouldn't believe him. She heals your Pokemon, and she tells you more and more about what would happen if Giratina would be left unchecked, and explains why both worlds (your world and hers) are distorted. Tell you that you need to either defeat or capture Giratina to finally stop the craziness going on.
Appearance 9: She appears again after you catch Giratina. She tries to reason with Cyrus yet again, this is to no avail, and he leaves. Cynthia meets up with you again in Sendoff Spring, thanks you for helping out, and she leaves.
So, Cerberus, where does that leave us? It's true, I will fully admit that I overlooked one thing and one thing only: Lance battles Team Rocket with you....once. And only because he figured it was necessary at the time. Cynthia has not, she's far more interested in studying about Pokemon and how they came to be, their origins, and everything else a Pokemon Researcher consists of. The other reason why Cynthia doesn't help you to battle Cyrus is relatively simple: it's your journey, not hers to take. She could very easily manhandle Cyrus (the same way Lance manhandled Silver, apparently), but she chose not to because you'd be better off for the job.
However, again, visiting your main point, does Lance do more in Rocket Hideout than Cynthia does in the entirety of Platinum like you claim? I heavily disagree and this is bordering on actually being really false. Keep in mind that I'm discounting Cynthia's many other appearances throughout the game so the player becomes more and more familiar with who she is and her general character (we know she has family, as evidenced with her giving you the Old Charm to give to her grandmother, therefore fleshing out her character more. Lance also has family, what with Clair being his cousin and his grandfather being the elder of the Dragon Masters clan).
If you're going to claim something like one champion does more than another, make sure the games actually support your claims and that you're not spouting nonsense. As I said in my previous post, Cynthia is a Pokemon researcher and she likes sharing her findings with you. Whether you find that meaningful or not is irrelevant, but she does so anyway throughout her myriad of appearances in Gen IV. Now, it can also be said that their overall contributions are just about equal, however I'm having a hard time dismissing the fact that, again, Cynthia appears many times on your journey in D/P/P to inform you of things or to help you out with small things here and there.
Now, in regards to Team Rocket HQ vs Distortion World, it doesn't really matter because either way you compare them, you're doing the majority of the legwork. You have to figure out Distortion World mostly alone in the same way you have to figure out Team Rocket HQ mostly alone. It's not like Lance follows you all around Rocket HQ and holds your hand (neither does Cynthia in Distortion World, if you're about to retort with that), he tells you what you need to know that's relevant to the situation (the same way Cynthia tells you what you need to know about what's relevant) and and he goes on his way.
tl;dr: If we're comparing Distortion World vs Rocket HQ as far as overall champion guidance and helpfulness, they're just about equal. If we're counting overall contributions to the entire game, Cynthia easily makes more contributions and appearances than Lance does, and that's simply a fact, because Lance doesn't appear during the main storyline otherwise except to watch you fight the Red Gyarados, and Cynthia's "contributions" are moreso along the lines of providing you with backstories and explanations behind Pokemon. You may say that her contributions aren't grand in the entire scheme of things, and I would agree with you 100% on that, except I'd rather a champion that would appear many times so I can get to know her better as a character than a champion that appears only for a certain segment of the game and then only re-appears as champion.
