I'm not sure that handheld LCR meters are any more accurate than a good DMM with capacitance support from brands like Agilent or Fluke. I've personally tested many and am completing a performance test of the 1252a and 87V meters, and they are on par. Alas, I've never used those super expensive ones to act as comparison. But dedicated handheld LCR meters aren't any better than 1%, which at least the 87V or the 1252a are too. Where LCR meters excel is the added calculations done like quality factor, ESR etc., and particularly easier uH measurements.
As tekfan says, calculating capacitance to any better resolution requires far more advance techniques, and such meters suddenly jump from $150 DMM types, to $21,000+ types.
In the 20+ years I've owned Fluke 80 series DMM, they changed the method of calculating capacitance, the early one were just RC time constants using old board timer and constant current; its described in the service manuals of the generation 1 and 2 Flukes. Model 3 and up use a method now common today even in lesser brand DMM and LCR meters, but where they differ between brand names and no-names is the quality of the implementation. But none I've seen have gotten >1% at best for accuracy. if done right.