ADS1256 from TI has eight single-ended 24bit channels with high-impedance input buffer and PGA. OpenEXG project has PIC code to interface it (they use two channel version ADS1255, but it should be the same).
If you want differential inputs, then there is ADS1298, with 8 channels, PGAs and A/Ds, internal reference, plus ECG/EEG circuitry which you can ignore. I am not sure you can find any example code for this one, though.
If you are looking for resolution, then precise, low noise reference is a must.
The name is a clue. "Microconverter". You can consider this an ADC/DAC with a microcontroller peripheral attached rather than a microcontroller with peripherals. The (semiconductor) process used is more optimized for precision analog than trying to fit analog bits into a digital process and ending up with mediocre analog performance. For example, the reference has a tempco of 15ppm/K (typical) and is accurate to +/-0.4% maximum. Not great numbers, but better than most of (say) Microchip's offerings. That said, this is a very old chip (over a decade, IIRC) and each year the cheap/high volume ones tend to get a bit better.
So the main difference is the performance of the analog bits- reference, ADC and DAC will be closer to that of similar discrete devices (they're made by a company known for analog prowess).
You can also get models with "24-bit" ADCs, and an ARM core.
The advantage of having several chips combined into one are less board space, easier to get going, less parts on the BOM. Disadvantages are that the cost will probably end up higher, and the performance lower than a solution designed with separate chips. If the chip gets discontinued and you've designed a product (or an entire product line) around the chips, you may have bigger problems than if you went the other way.
Best Answer
There are many many many many excellent existing on web tutorials on this.The following are excellent examples BUT you should have a look around as much has been written that will improve your general understanding far more than having people spell out again something which is so well covered elsewhere.
This one gives a better than some concise explanation of 3 types of ADCs complete with flow chart where apposite. Remarkably compact explanations but easily enough followed with only a basic grasp of electronics, if that.
The same people also offer this superb introduction to digital to analog conversion.
From the above pages: Successive Approximation ADC
Note that a DAC is used in the ADC :-) - see DAC below.
Illustration of 4-bit SAC with 1 volt step size (after Tocci, Digital Systems).
The successive approximation ADC is much faster than the digital ramp ADC because it uses digital logic to converge on the value closest to the input voltage. A comparator and a DAC are used in the process.
One way to achieve D/A conversion is to use a summing amplifier.
This approach is not satisfactory for a large number of bits because it requires too much precision in the summing resistors. This problem is overcome in the R-2R network DAC.
__
The summing amplifier with the R-2R ladder of resistances shown produces the output
where the D's take the value 0 or 1. The digital inputs could be TTL voltages which close the switches on a logical 1 and leave it grounded for a logical 0. This is illustrated for 4 bits, but can be extended to any number with just the resistance values R and 2R.