So our two positions are:
"There's no way JumpShip transmission is cheaper than HPG transmission."
and
"There's no way HPG transmission is cheaper than JumpShip transmission".
If we're to continue, then the only thing to do is start herding up some catgirls for the slaughter. Perhaps we might also light the *Cray Beacon* in order to possibly get him or someone else to chime in and spare the innocent lives.
Let's start with some quotes:
The two types of HPGs available for star
systems are A-rated and B-rated. Both
classes of HPGs have a 50-light-year
range. Serving as communication hubs for
B-rated HPGs, an A-rated HPG transmits
to each B-rated HPG in range sequentially
every 12 to 24 hours (sooner for priority
messages and during the Star League).
B-rated HPGs transmit less frequently
than A-rated HPGs (every 12 hours during
the Star League, or every few days after
the fall of the Star League).
So HPG transmission propagates roughly 50LY every 24 hours.
I'm assuming we don't need a quote to agree upon how JumpShip traffic works, can we agree that it's 30 LY per jump, and it normally requires 48 hours for a quick recharge from a charge station and some amount longer than that in most star systems via solar sail? But for the sake of comparison let's be crazy generous to the JumpShip system and presume the "average" delay between jumps is only 2 days. That makes JumpShip propagation roughly 30LY per 48 hours.
So to keep the catgirl genocide on topic with the OP, let's use a hypothetical example of the New Avalon Herald wanting to make itself available on Annapolis in the Draconis Combine. The distance between their respective X,Y coordinates is just over 262 LY. Presuming equally for HPGs and JumpShips both that a hypothetical perfect minimum distance path is possible: that's 5 HPG transmissions taking ~4 days to arrive. Via JumpShip that's 8 jumps, taking at least 14 days, not including DropShip travel time. And when factoring in DropShip transit times, the HPG transmission arrived before the DropShip leaving New Avalon even reaches the JumpShip.
Even before factoring in relative C-Bill costs, if time is at all a factor (like say getting your newspaper broadcast out before its contents are irrelevant upon receipt) HPGs are obviously the way to go. With the downside of ROM potentially reading your mail, granted.
We've also got the problem of hiring out not just a DropShip but a JumpShip as well (or multiple JumpShips if you want to go faster and do Command Circuits). If you're just waiting for the next free trader going in the right general direction to sell you some passage for your cargo, it's not reasonable to continue to presume minimum times anymore. For minimum times, you have to hire out entire spacecraft, which has got to be crazy expensive for something like delivering the newspaper or a trideo episode. Even before we start arguing about what the exact C-Bill costs would be either way.