Which precision rectifier should I use for a 60dB LM3915 Vu-meter?
A full wave rectifier copes a little better for low-frequency signals than its half wave counterpart.

However, what constitutes a low frequency? It depends on the input range.

I shall assume this is for audio - and I've worked a lot with the LM391X range - so I doubt you will see any noticeable differences between the two. In all likelihood, the frequencies that start to give detectable differences in the output will be cut out by either the source of the audio or your pre-rectifier circuitry. 

I highly recommend reconsidering your use of two 3915s - instead use a 3915 (for the lower values) and a 3916. The '16 version is identical except for the "spacings" of the dB indicators - IIRC it's +3, +2, +1, 0, -1, -3, -5, -7, -10, -20. This actually represents an 'industry standard' VU meter, as you get a greater resolution from the +3 to -3 range - 6 LEDs instead of 3. If you ditch the -20dB pin, you set the highest pin of the 3915 to be at -13dB, to give a linear progression of 3dB per LED from -7dB down. The 3916 datasheet (and the '15, briefly, I think!) shows an example of such a circuit, including a level-shift amplifier so the lowest dB indicators aren't triggered by noise.

Of course if you're just building something for fun then stick with two 3915s. If you are going to stick with that though, at least have a look at the 3916's datasheet. It includes two/three more rectifier circuits, one of which conforms fully to the DIN specifications for a genuine VU meter. At the very least it has a few more paragraphs to help you choose, even if it ultimately convinces you to use the simplest half-wave rectifier!