I haven't tested as sufficiently as the OP, but I discovered firsthand that the Everdrive GB x7 consumes more power than a standard cart. If I had to guess, I'd guess almost as much as the EZ-FLASH Junior.
My modded GB Pocket wasn't able to use either cart until I replaced the batteries with lithiums that boasted 1.5v output.
My modded GB Pocket wasn't able to use either cart until I replaced the batteries with lithiums that boasted 1.5v output.