I guess this is a bit more of a question of what you're looking for, you say you're into contests so, that's something both judo and karate have in an abundense (kendo isn't lacking either but those two just stand out in that field).
So lets say we're down to those two ok?
now it boils down to the question of what you want to improve:
1) If you're looking to go into MMA or more street like self-defence+ major confidance boost striking is a must, not an option, just ask Gabriel Kitober; went into MMA as five times champion in BJJ but got his A$$ handed to him by a guy who just low-kicked him to the ground in the 9th IWC (though in his defense I will say that when he took the guy to the ground he nearly killed him), judo would improve your stand up grapling which should be desent if you're sick and tired of BJJ but karate has some of those elements as well (depending on style).
2) If you're looking to improve your grapling (and putting on a few pounds of mass) than look no further than Judo, it would imensly improve your stand-up grapling with its throws and it also has a few things you might have picked up in BJJ, so you won't be too much out of your element.
Also all of the Judokas I know are rather large and well built, so i'm guessing the two are connected.
in general if I had to grade these two arts it would go like so (scores are given out of ten):
karate
Stand up striking: 8.7
stand up grappling: 4 (some styles have good elements but others are completely lacking hense the score)
ground work: 2 (only ippon finishing blow if i remember right)
judo
stand up striking: 2
stand up grappling: 9
ground work: 6 (from expeirence sparring against two brown belts and one black belt in bJJ)
these are my own personal scores and they are I admit subjective to my opinion so feel free to state otherwise if you think so


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