Difference of Hapkido and Aikido
The first difference is that Hapkido includes much of kicking techniques while Aikido doesn't. The highly developed kicking techniques characterize identity of the overall kinds of Korean traditional martial arts; Taekwondo is most famous for that and the best.
The second difference, which comes from the first naturally, is that the former has better balance in its technical system than the latter. If you have no training of kick you cannot use it even when you have better chance for that; It means, you come to be contrained within useing hands or another parts. Of course, it is not always disadvantage; If you have too many techniques you can be confused what to try sometimes. From the TAEWKONDO point of view, every technique converges to Ilgiyae. But if you didn't obtain the ultimate goal, you had better to concentrate youself on small number of techniques.
The third difference, which comes from the foregoing two, is that Hapkido use the full principle of Kang as well as Yu. They suggest Aikido use only Yu principle in my observation, but as far as we formalize Yu as that of 3JKY (and I cannot find another kind of useful and meaningful formalization) no martial arts can be a martial art with only the principle of Yu. I admit Aikido is very wonderful martial art and then, I come to conclude that most people of Aikido don't recognize their foundation. Hapkido man also emphasize the principle of Yu, of course without full understanding of what it is, but they don't concerned with Kicking. They know Hapkido includes Kang principle too.
Any way, summing up this short comparision, I can say that Hapkido includes techniques of Aikido in its entire technical system, and Hapkido is a more generalized martial art in this sense while Aikido has maintain its own uniqueness in its system.