As noted above, the Big 3 legacy alliances are generally monkey see, monkey do in terms of fare filings (see below for comparison of NYC-FCO cheapest biz fares on UA/DL from EF -- note that EF fare quotes don't include YQ/YR and taxes). But they don't try really put much effort in trying to match pricing/fare bucket availability on any given day. On some days, one alliance might have flights with availability in lowest buckets while others do not. And vice-versa on other days. A few random searches won't really tell you much.