I've taken the liberty of testing those two throws for a bit and I did manage to come up with something.
First off, his down throw appears to be the more usable of the two. For example, if an opposing Mario fails to DI, it can be used to set up a tech chase between 28-70%. This is especially notable because unless the opponent specifically DI's down, 90% of the cast will be able to jump out of a grounded cargo down throw even at 0%. That being said, if they DI up for the down throw, this setup doesn't work against anyone.
Up throw is... something, alright. It deals less damage and has more BKB than cargo up throw, but never kills, so finding a legit use for this move was pretty tough. Unless I missed someone, it can be used to set up a tech chase on Battlefield's top platform against a grand total of two characters: Ganondorf between 0-1% and K. Rool at only 0%. For whatever reason, a grounded cargo up throw in that tiny percent range won't send Ganondorf high enough to land on the platform despite only being the fifth heaviest character. On the other hand, K. Rool DOES get sent high enough, however a grounded cargo up throw just won't send him into tumble at 0, while a regular up throw will. Yeah, I have no idea why this is only a thing for K. Rool, but it just is. Hey, at least we can say Jigglypuff's up throw is worse!
As for follow ups, you can punish a missed tech from down throw with a down tilt or jab 1 into Giant Punch or down smash if you don't have one charged, while dash attack can be used to punish tech in place or tech away depending on the character and stage positioning. Up throw was a bigger question mark, but after some testing, I found a couple missed tech punishes. Against K. Rool, you'll want to full hop neutral air into double jump sourspot back air for the jab lock, then finish it off with a Spinning Kong, dealing 56.4% in total. I couldn't seem to land the sourspot back air against Ganondorf (though I may have just been timing it poorly), so I instead went with full hop sweetspot back air for the jab lock into a buffered double jump down air, which deals a still respectable 45.6%. Unfortunately, Ganondorf can jump before landing on the platform again, so you won't be able to extend the tech chase unless your opponent isn't paying attention. Finally, neutral air is your best bet to cover their options if they manage to tech due to its lasting hitbox.
I've said a lot already, but if anyone has anything more to add, please do!