I'm curious as to why dual-slope analog to digital converters are used in most digital voltmeters, like one of these when a delta-sigma converter like one of these easily exceeds the specifications of any of the other dual-slope converters sold by Microchip, and in fact many other suppliers, especially given the low price point of the chip (about $4 in low quantities.) Is there a reason I am missing?
With a dual-slope ADC you effectively get free averaging as the run-up integration phase will have this effect. The output is also extremely simple, just a pulse that needs to be timed which can be done with even the simplest micro controllers.
$4 is a really big deal when your making 50,000 of something and trying to sell it for $50. The dual-slope part you linked is $1.64 in a PDIP for 5000+. The sigma-delta's cheapest package is $2.88 in its cheapest package. Saving ~$1.20 on a single part AND being able to use a more basic microcontroller is a big cost win.
I think you'll find the more expensive multimeters do use higher end ADCs.
Incidentally, an approach I used once that seemed to work pretty well was to have a PIC output drive an RC circuit and feed that into one input of a comparator, while the other input of the comparator was the signal under test. Every 100us, I would sample the state of the comparator, set the output high or low as appropriate, and (if I set the output low) bump a counter. Every 4096 interrupts, I would copy the value of that counter and reset it.
The beautiful thing about this approach is that provided the input isn't changing, and provided the RC time constant is sufficiently high, and the input isn't too close to a rail, one can avoid any need for precision constant current sources or other such things. The system will output a ratiometric measurement of the input voltage compared to the output rails feeding the RC (e.g. if the input voltage is 3/4 of VDD, and the output swings fully to VDD or ground given the currents involved, the reading will be 3072/4096).
The biggest problem I've observed with this approach is that if the input changes significantly, the readings will be pegged for a little while, and the first reading after that will be meaningless. Still, it's a cheap approach and seems to work pretty well.
It's basically speed, resolution and cost, dual-slope converters are cheaper but a lot slower and offer lower resolution. Speed and high resolution don't matter for something like a DVM, but they are important for, say, sampling speech and music.