Hi testered,
That is correct.
If the focal length of the lenses are the same, it should be the case. However on this type of camera, the focal length is quite short, even at full zoom so the depth of field is not particularly shallow anyway. The factors that reduce the depth of field are a wide aperture (small f number), a longer focal length and close subject to camera distance. Google the subject, there'll be plenty of tutorials to read.
Why not do some test shots to compare the 2 cameras. You probably won't see a great deal of differnce. You need to take shots of a receding scene that has definite makers like fence posts, or at closer distances, looking along a ruler.
Terry

For really narrow depth of field, you will need a digital SLR with interchangable lens and a large sensor. Most consumer cameras have a very small sensor and therefore short focal length lenses, which often results in everything from 5 ft to infinity being in fairly good focus. If you are wanting to explore the artistic possibilities of narrow depth of field, you will want to move up to an SLR. Canon digital Rebels might fit your needs.

According to the specifications, the SX30 and the SX130 both have DDC sensors that are 1/2.3 (less than half an inch), so neither would have a very narrow DOF, but the SX30 has a f2.7 lens, and the SX130 f3.4, so the SX30 would have a slightly narrower depth at f2.7. Still, since the sensors are so small, compared to an SLR, I don't think you would get the effect you are looking for. You, by your question, have entered the world of wishing to do more "artistic" photography, rather than just "snapshots". For those who are content with snapshots, it's usually an advantage to have most everything in focus at the same time, so this "feature" of point and shoot cameras allows amateurs to shoot an in-focus photo most of the time. (If they can manage not to move the camera. And the IS even helps them if they aren't so steady). Sounds like you've gotten the bug (shutterbug), so you might as well start saving up for the DSLR. They are getting cheaper every year.

Jeff