@Krodal:
Brand : TakeMS 2GB ( some years old, though )
Power consumption: not sure how to measure the actually required power spikes during write. I don't have a real oscilloscope.
Is analogRead fast enough ? If yes, should I use a second arduino to measure, or dig into how to do this interrupt driven.
Bad breadboard connections: I understand both reading and writing uses all SPI signals, and reading works well...
@MarkT:
Speed: I'm testing based on the Arduino SD library and tried both
card.init(SPI_HALF_SPEED, chipSelect); // as used in CardInfo.ino example and SPI_QUARTER_SPEED. Is it possible to be too slow with my 8MHz board ?
LevelShifting : I understand both reading and writing uses all SPI signals, and reading works well...

Is there power drawn from the MOSI or CLK line ?
The adapter provides 10k pullup resistors between its 3.3V regulator and the signal lines,
so I just added small reverse diodes to my 5V atmega signals, providing 0.6 .. 3.3 V signal level to the SD card.
Thanks to both for your feedback so far.
More hints ( especially regarding live power measuring, and whether this makes sense ) are very welcome.
My next step will be to cross over the available components
A ) Arduino Uno with Adafruit DataLogger shield ( working )
B ) Standalone 8MHz with
LCstudio SD card module ( read only )
and see if problem is rather the 8MHz no crystal or the SD card module side