The LTC1968 is better and cheaper but not as cheap as crap meter with alleged RMS capabilities.
There AD737 may not be a good solution for a handheld meter. It is made to also work with a rather high supply and this way is more something for a mains powered bench DMM, not so much for a handhelp with a 200 mV signal range.
Another weak point of the AD737 is that it's settling speed depends on the amplitude and with low amplitude it gets very sluggish.
For a battery powered meter I would prefer the AD8436. This one at least removes the dependence of the response time on the signal amplitude, but still suffers from a BW that depends on the amplitude. So one has to chose between a limited BW or nonlinear effects from variable BW.
The LTC1968/1967 don't have the amplitude dependent BW, and as it looks like less temperature effect, but the linearity at small values seems to be a bit worse. So I won't call it a clear winner on either side.
Some of the cheap meters use digital RMS as a 3rd method to do the RMS conversion. This should give good temperature stability, good linearity and a faster (FIR vs IIR type) response than the AD8436 or LTC196x (the AD737 is even slower). The down-side is often a limited BW (e.g. 1-10 kHz rang), but at least amplitude independent. The actual implementation may still vary, but much is part of the chip sets and thus no so much to go very wrong.