I have to agree with Peter Sillery, the Boss chromatic tuner has never let me down, I think it is even more accurate than the one they build in the GT-6B. Over here it will set you back a cool 125, but is well worth it

I would venture to say that the smaller is probably a little more accurate, as the bigger one looks like the tuning pitch can be adjusted. Most guitar/bass tuners I've found will tune based around the "A" note, which is generally 440hz however, some tunings allow for the A to be tuned at other frequencies, the other most common to be 445hz. With that said, your other strings would be tuned relative to whatever frequency the A is set at.