I find that in Chrome, which is a faster browser, that transitions are much smoother than in Firefox. I think I would look at the file size of the image you’re uploading. Do the pixel measurements match what your Genesis Responsive Slider is set for? Also, with Genesis Responsive slider, if you change your slider settings, sometimes it helps if you re-upload your featured images. I think the actual file size is large because it takes quite a while for the page to load. You can check that at tools.pingdom.com
You can see there that your homepage-images-1button03.png and its counterparts are pretty big. They’re PNGS so they’re relatively lossless.
If you were to use JPGs there and not superimpose the text with an image but rather take the post content-limit and work on the styling to get the transparent dark background, you’ll have mush smoother transitions.
Check these:
http://dentonbanter.com/
http://bondurismusic.com/
http://criveraworley.com/
http://criveraworley.com/
http://tcgihost.com/~rhumc
http://oconnellfirm.com/
All are set to fade but still have smooth transitions.