I've not come across the PuckPuck before but it looks like you're comparing slightly different things as the French press has constant contact with the grind whereas the dripper stops brewing once the water has passed through. I'd be tempted to try it on the slowest possible setting to see if you can recreate it, or mess with the grind size and amount to slow down the flow rate.
For my money I don't think you can beat one of these for making cold brew.
I've not come across the PuckPuck before but it looks like you're comparing slightly different things as the French press has constant contact with the grind whereas the dripper stops brewing once the water has passed through. I'd be tempted to try it on the slowest possible setting to see if you can recreate it, or mess with the grind size and amount to slow down the flow rate.
For my money I don't think you can beat one of these for making cold brew.