With regard to sparring, it is very difficult to apply what you know to a situation where the other person has a completely different aim to you. I used to be very interested in how I would compare to a practitioner of a different art, but really aikido is not suited to a situation were somebody is try to pick you off or tap you on your nose. Plus a karate person (for example) will never commit an attack or close in when they see you aim to enter and apply technique. This can be very disheartening and probably best avoided.
It is really strange to hear you say that because a few of the people I know who have dan grades in both Aikido and Karate seem to say the opposite.
One guy said that the body movement and getting off the line he learnt in Aikido meant that he walked all over his opponents during Karate competitions. All he had to do was move off the line and attack from a different angle, most of the Karate guys were very linear and were not used to having an opponent who was not in front of them.
Admitedly we do a fair amount of Aki-Jitsu in our class, but we do a lot of defenses against punches and kicks. Is this unusual for Aikido ?