Well it depends on a few things. One, was it made "Internal" storage on the old device or just left as the standard "External" storage. I ask, because if it was made "Internal" then no other device can view anything on it, ever, unless it is put back to "External" through the original device, and then it would remove anything on it anyway.
Also, the new device has to be able to accept the size (storage capacity) of the SD card. So if that card can't handle the size then it won't be able to read the card correctly.
What is actually happening when you insert the card into the new phone?