Hello, my friend.
I've been cross-training from Kukkiwon Taekwodo to Shotokan in the latest months (I've studied Shotokan for sometime before and I just don't see myself today not going back to karate -- not that I'm going to abandon taekwondo anyway), and I think the cross-training for one who's already ok with taekwondo is a great idea.
The similarity between both arts will make it easy to grasp a lot of things on karate. If you are a KKW practitioner, maybe you'll have a little trouble on the specific way to perform some movements: stepping and turning (the subjects discussed in the thread I started recently -- Kukkiwon does it in straight line), and also the blocking techniques (uke waza / makki). Possibly if you don't change your way of doing things no-one will notice, but the differences could also be a little annoying: if you get used to the karate ways it could confuse you when you do your taekwondo 2nd dan grading test.
Specifically on the uke waza/blocks (the stepping part can be seen more in depth in the recent thread in this forum), the main difference is that the blocks in karate are
usually performed with a "reverse" hip rotation (when compared to taekwondo), and the finishing position is with trunk slightly turned to the side, while in taekwondo we usually finish the technique with the trunk totally looking forward. I just don't know why taekwondo does the hip rotations like that, and I honestly prefer the karate way, as it fits better most applications I have in mind (the hip supports the hiki-te/pulling hand and the turned position makes you dodge the attack instead of putting you directly in front of it). By the way, I was just thinking of starting a thread on the difference of both hip rotations and asking the pros and cons of both ways.
One thing that is very usual in karate dojos is some stiffness of karate-ka, that is a bad habit that has become common in many places. Don't be trapped by that. Karate -- even shotokan karate -- is not meant to be stiff, and you should be as soft as in taekwondo, tensing your body only in the appropriate momments.
One other thing that you may see is the more frequent use of hands, that's something great I found when cross-training. But in the other hand, the upper limbs are frequently not used the best way, in my opinion (off course not in all dojos). I believe competitions have influenced highly shotokan practice, and because of that it is possible you see a great use of hands, but yet sparring from long range anyway (like starting from a distance, getting in with a few punches and then going out again). If you are concerned with self-defense applications, this doesn't seem a good way of sparring, in my view (even in taekwondo I believe in training for all ranges, but usually give special attention to medium and short).
If you haven't already gone in-depth into bunkai (forms applications studies, roughly speaking), maybe now it is the time. Kata is the soul and essence of karate: all self-defense and fighting principles and techniques can be taken from kata, if you interpret it correctly. Anyway, don't fall into close minded postures of admitting only one application for any part of forms, no matter how good it can be. From my experience, with taekwondo it is much harder to have the instructors accept there are many applications for one technique (example, "down block"), they'd just say "a block is a block". In karate, also from my own experience, this is at least less likely to happen -- I mean it is more usual to see instructors accept there are various applications for most movements, even if it doesn't mean the practitioners dig a lot into getting to know them. While in taekwondo this is some kind of controversial, in karate this is a largely accepted truth. But in all of this YMMV.
Only one last word on bunkai: in my opinion, the principles behind a technique in the kata are as important as the technique itself, or more. Once you understand the principles, you can adapt the movements, you can vary them and you'll be able to use in more different ways and more naturally. And off course, even if it's not "official", that bunkai thing can be done with taekwondo forms (no matter the set/organization/style) as well. However, I must admit I prefer karate forms when I look for applications, and I believe Kukkiwon forms were probably not created much with that part in mind -- instead, it was more on making a gradual progression for learning the techniques and combining them (which is a reasonable idea, nevertheless). I hope not to start another war on this subject, if someone gets ofended with what I just said, I apologize previously, and want to state that all of this is just my opinions and I believe I could be wrong
(and people are free to correct what I'm saying, although it'd be good not to hijack the thread).
I hope you have a great time with your cross-training.
