The ULN2003 looks a lot better.
Now the matrix is not wired like the data sheet is it.
The data sheet shows pins 9, 14, 12 & 8, 1, 7, 2 all being anodes. These anodes should be connected to the arduino outputs.
The data sheet shows pins 13, 3, 4 & 11, 10, 6 as all being cathodes these should be connected to your ULN2003.