How many dbs i will gain with 0,6mv cart.vs 0,3mv?

Shelter 501 at 47k ohms. I ran mine at about 100 ohms. I'd try that soon. 47k is more what you would use with a MM not a MC FWIW.If you have to, years ago I remember attaching 1/4 watts directly to the back of the cartridge when I needed a 10k load for a grado.

I will warn you that Koetsu over estimates the output of their cartridges. The Black is probably closer to 0.42 mv.
When I switched from a Koetsu Rosewood Signature (with a supposed output of 0.6mv) to the Shelter 90X (0.6 mv), I got an increase in volume, albeit not a lot (maybe 2-3 db).

However, I agree with you that it is convenient to have the volume control match between the two sources. I hated switching from LPs (where the volume control was at 12:00 for normal listening volumes) to CDs, (where the volume control was at 9:00 for normal listening volumes), as I always seemed to forget to turn the volume down first.
(It was kind of like getting into your car in the morning and the radio is blasting, whereas last night when you parked, it seemed okay.) :-)

Good Luck!

Since your new output voltage is twice your old voltage, the gain is 20 log (V2/V1), which is 20 log (2), which is 6 dB. So you would get an additional 6 dB of gain from switching cartridges. Looking at it another way, you would need 6 fewer dB, or half the voltage gain, to get the same volume output.

6dB, but why is this a problem? Why does the phono have to be at the same volume setting as the CD player? It is generally agreed that the further up the volume control is the better so the CD player is really the problem.

If you like the Shelter just turn it up a little and enjoy it.