I would recommend upgrading your struts at the same time. Lowering springs put extra stress on struts and the stock units will not last as long with the springs on. The reason I say to do the struts with the springs is to avoid having to replace the springs now and then in a few thousand miles replace the struts, which will cost double the money if you have someone else install them. If your struts are pretty new(less than 15k or so) you can try and run the stock struts with the springs and try your luck, I know of one or two guys that have run stock struts with springs with no probs so far. For cost and time sake though, change both at the same time.
The difference between Koni's and KYB's is that the Koni's are adjustable and are supposedly a more performance oriented strut. From what I have read, the KYB's aren't worth the money, just spend the extra money and get the quality Koni's.
BTW...next time you are stuck with a problem, use the search function at the top of the screen first and see if you can find an answer before you post a topic. Some of the members(Perry

) get a little "upset" when people don't put the legwork in to try to find the answers for themselves.
HTH