I don't think many aikiweb members have experience with kyokushin. That's why I respond, even though I only have a little experience in both arts. I've only been practising aikido since 2010 and I practised kyokushin for half a year in 2011.
I like both arts. They are quite different. Obviously aikido generally uses softer contact in training and it tends to focus more on defense than offense.
In kyokushin you accept that you will get punched and kicked. Your training toughens your body to a degree that it can take some punishment while you try to deliver more punishment to your opponent. I think aikido spends more effort in trying to avoid taking punishment. But even tough I'm not built like a fire hydrant, many are in kyokushin as well as in aikido.
I liked kyokushin, because I wanted to know how to punch and kick and how it feels to be punched and kicked, without getting into bar fights. Kyokushin offers a controlled environment where you can challenge and test yourself. To some degree, because there's no grabbing, no holding, no pushing and no punches to he head (only kicks). Other than not punching the head, wearing a gi and thin gloves or no gloves, and having a very strict etiquette and morals, I think kyokushin is quite similar to kickboxing. I know many from the dojo where I trained (http://www.karateclubnoritsu.nl/
) went to kickboxing, came from kickboxing or did both. Kickboxing happens to be quite popular in the Netherlands (we even had a few K1 champions).
I only trained for half a year, so I was still only a beginner when I quit (red belt). But at least I did get some training in punching and kicking. In aikido class we hardly ever train it. If we do, it's usually a class from a teacher that has some background in karate or kickboxing.
Kyokushin classes tends to give you a lot more bruising than aikido classes, especially in the beginning when your body hasn't toughened yet. After a year or so, it gets better (or so I'm told) but I think bruises will always be a part of training, even for advanced players. Bruised thigh muscles from not blocking low kicks, bruised forearms from blocking punches to he body, and may other bruises. Sometimes also abrasions of the knuckles from training bare knuckle punching on cushions. But these bruises are usually superficial, and they fade away within a couple of days days. Anyway, I always felt great after class!
All in all, I think aikido and kyokushin are almost opposites. But I enjoyed the combination while it lasted.