The 7870 and the 7850 had both lower performance. The 7850 is cut down as well as it runs at a lower clock, the 7870 (at least the reference, there were plenty of faster OC models around [afair up to 1.2GHz], but I guess AMD wouldn't use those) is simply clocked lower than the 270X.And they give a 2.8 perf/watt increase here as well, against a chip that's now 4 years old and for sure was sold in higher performing configurations with less wattage (HD 7870, 175w or HD 7850, 130w, IIRC).
The 270X runs at 1050 MHz and 5.6Gbps memory, the 7870 only at 1000MHz and 4.8Gbps memory.