Hi Steven,
As far as I know (no personal experience here) katana blades are stiffer than European blades, being relatively thick at the spine. Also, the way they are mounted tends to dampen vibrations quite quickly. So It's normal that you can't see a wobble in your katana, while you can see one in the longsword.
What part of your blade were you using?
I have seen one of my own swords bounce (even did it on purpose to test ideas

) when striking a hard target such as a plywood plank resting vertical on the ground. On this kind of hard, unyielding target, striking too far from the node of vibration on the blade (the place where it does not wobble) can produce this result. Basically the blade buckles under the hard impact and starts vibrating, if the part that bit into the target moves too much it jumps out and foils the cut.
Often it is composed with another effect: when you strike too far from the center of percussion associated to your hand, the impact produces hand shock, and then the sword bounces back against your hand which ejects it from the target. Did you feel a kick in your fingers at the moment of the impact?
If you strike near the tip with a longsword, you'll probably see both of these effects. These strikes will work very well on softer targets though... A katana has the center of percussion further towards the tip (well, I think it should

At least training sabers have it), so perhaps you struck at that spot, and since it is more rigid too it doesn't give the same vibration problems...
Well that's my experience but it's hard to say for sure without comparing the swords...
Regards,