That's just not how the media works, for anyone, ever.
Ask anyone who's ever worked for a record company or PR company, even quite minor celebs have press deals made over them all the time. It's absolutely standard for record companies to offer juicy stories about less important clients in exchange for the press agreeing to not publish a potentially damaging story about a client they want to protect. It happens all the time at every level of fame and in every medium, music, film, reality, royalty.
The press would not ever turn around and print both stories, because then the company in question would never cooperate with them again and would have the specific media outlet or specific journalist blacklisted and removed from their PR invite list, and they don't want that. It's a deal and it's how the media works and everyone who's ever worked in the media even a little bit can confirm that.
Besides the relationship between the press and the royals is a tricky one. The media has always picked one person to demonise and turn the centre of a scandal, if they were just chucking out scandal and negative articles all the time about different members of royalty at random then they'd develop a reputation for being anti-royal, and the demographic of most newspapers (except for the Guardian) skews right wing and broadly pro or neutral to the monarchy. The press want to balance creating enough controversy to sell papers while not pissing off their core demographic, and they do a shitton of market research to find out exactly who is buying their papers and what they want and like. Most people who buy physical papers tend to skew older, and older people tend to have more respect in the institution of royalty. The press know they have to walk a fine line between engineering scandal to sell papers, and not pissing off their core demographic by being perceived as being anti-monarchy or having an agenda.
The press also love to needle people and write hinty articles when they think there might be a potential scandal without coming out and saying anything. They also write negative stories to try to force celebs and royals to do what they want (do more public appearances, for example). It's a constant tightrope with so many different factors and personal relationships built in. That's without getting into the relationships between different royals who all brief the press in their own favour, and sometimes have competing PR.
The papers would much rather have dirt on W than H.
No, they wouldn't. They really, really wouldn't. Not unless it was grade A dirt with solid gold evidence. Again, this shows lack of experience working in a newsroom. Harry sells far more papers than William and is generally considered far more scandalous, better clickbait, and more fair game for scandal (the whole pissing of your core demographic thing - the press can write can only go so far in being negative towards the next King without offending the part of their demographic who are pro-monarchy), and they can write whatever they want about Harry without alienating or being blacklisted by the Palace. They'd need solid proof of major scandal to write something genuinely scandalous about William and there clearly isn't any. They can report on stuff they can twist into William failing to do his job because that way it sounds like they're defending the institution of monarchy and not alienate their core demographics.
I know I'm on record as being hardcore republican but I have worked in the media and news for many years, never in royal news admittedly, but I've seen these kinds of media deals being made over actors and singers lots of times.