There are basically two different markets for ADRs and ordinary shares. 1) The American market, 2) the "local" market.
The following is not true for most stocks in "developed" markets. But it is often true that the American market (for ADRs) is far more liquid than the local market for ordinary shares of a developing country. For instance, there was a time when the ADRs of Telmex (Telefonos of Mexico) was the fifth most traded stock in the world, after Exxon (before its merger with Mobil), IBM, Microsoft, and A T&T, meaning that it was easy to trade with low fees on the NYSE. It was much harder and slower to buy the local shares of Telmex in Mexico, on the Mexican exchange.
Also, the accompanying currency transactions were harder to execute with the ord, because you have to settle in local currency and pay an FX commission. With the ADR, the exchange rate is "built" into the (dollar) price, and you settle in dollars.