This should be answered formally by someone who you are paying and who signs his opinion and can be held accountable for it - or ata least who specifically states their qualifications, competence and degree of culpability in the event of subsequent "issues".
There is more to this than can be answered without a deeper level of understanding than your abstraction will allow and than can be even partially answered well, without many to and fro q&As, in this sort of forum. We'll try regardless :-).
" ... the more reliable the output (ie closer to the analog input). ...
Your use of the term "reliable" is non standard and demonstrates a lack of understanding of the process you are attempting to monitor. This is not meant to be rude - just factual. And important.
If you are making this instrument then somebody with a good degree of technical understanding needs to go over the proposal and design in detail. If you are buying it then the name on the nameplate is more important than the specs of the ADC. eg you can be about certain that if it say "Agilent" (and is genuine) then it will do the job well and be 'reliable enough' [tm]. If it says "eg "Golden Sparrow" you may wish to look elsewhere.
ADC resolution affects the potential accuracy of the result. As the required resolution increases the other factors which affect achieved accuracy and resolution become increasingly important.
- Example: I have a well built but low cost digital scale with a full scale reading of 500 grams and a resolution of 0.01 gram (10 mg). I can obtain about 300 mg of reading variation by holding my wristwatch about 30mm above it in one orientation and about half that when the watch is turned at 90 degrees. An electric fan heater with coiled heating element of about 150mm dia, when operated within a 100 mm of the scales turns them into a random number generator).
ADC technology influences susceptibility to external interference. Successive approximation, Flash, dual slope, ... all have pros and cons. A dual slope system will reject 50 Hz superbly if designed to do so but may fail miserably in a 60 Hz mains environment. RF interference (cellphones, mobile phones, pagers, wristwatches !!!, other instruments, ...) MAY cause issues. The ADC proper is part of this but the overall design needs to address the actual requirement.
Potentially more may be said if better information on actual requirement becomes available.
What country?
The dynamic range is the ratio of the maximum voltage to the minimum voltage that the ADC can convert. The maximum voltage is 5 volts. Since it is a 12 bit converter, it has a resolution of 212 - 1 or 4095. Thus the minimum voltage, for which the ADC would have only the least significant bit set, is 1.22 millivolts. So the dynamic range of your ADC is 5/.00122 = 4095 = 72.2 dB. In general, the dynamic range is only a function of the number of bits, not the maximum input voltage. But I calculated using voltage just to show you the details.
Best Answer
Either differential input can reside between 0V and AVcc (without potential chip damage) but, if you exceed a difference voltage greater than 2.2 volts then your digital result is out of range.
You should also note figure 32 in the data sheet that gives you an indication of the input circuitry and informs you where the 1 kohm differential input resistance comes from.
Theory of operation (page 17) also informs you that the inputs are each centred at about 2.4 volts with the expectation being that an individual input may impose up to +/-0.55 volts (1.1 Vp-p). Clearly both together give you a capability of 2.2 Vp-p as previously mentioned.
You should also note that gain error could make the 2.2 V typical value for full scale +/-10% different. Zero error can add or subtract +/-10 mV also so, if you expect to use it without calibration checks take into account the potential reduction in range to less than 2 Vp-p.