The Olimex ones are 10-bit (supporting both active and passive electrodes), while it's claimed[0] that 12-bit resolution is sufficient for EEG.
However, it's worth noting that there are obvious advantages to the higher resolution.
[0] https://www.biosemi.com/faq/24bitsystem.htm
As his link makes clear, your ADC just needs enough resolution to measure the signal when the (amplified) offset voltages don't saturate it.
The Olimex ones are 10-bit (supporting both active and passive electrodes), while it's claimed[0] that 12-bit resolution is sufficient for EEG.
However, it's worth noting that there are obvious advantages to the higher resolution.
[0] https://www.biosemi.com/faq/24bitsystem.htm