Well, I have just installed the SD bridge pickup. The specific pickup is a SD SJ5b 67/70. The one replaced comes from an Indonesian Squier ICS11xxxxxx. Edit: I have just checked and on the back of the DD PU it says: "JB105B BRIDGE 1103". It is covered in black foam, that is why I did not see it first.
Yes, there is a difference. My first impression is that the SD has more bass and more attack. I recorded a few sounds and then did a frequency analysis (Audacity) on both the SD and the DD recordings. Not very scientific, but in the graph you can see clearly that the SD has louder harmonics, while the DD has a skinny spectrum. Interestingly (i.e. I do not know what it means) in both pickups there is a solitary peak around 13KHz, but the SD's one is 10 dB louder than the DD's. Accepting that this is not an artifact, I would say that it explains the attack part of my perception.
On the other hand, I got more or less used to the DD sound, and I now understand why people like it. The recorded sound is quite usable, though I did not like it so much when played through my home amp (Taurus combo).
Now I have to find the courage to install the neck PU... I think I will get a new pickguard, not wanting to modify the one I got with the bass...
Thanks for your comments! And enjoy your holidays!