I did a few breadboard experiments, here's what I found:
74AC14, schmitt hex inverter, single gate oscillator with one extra gate as output buffer, powering a 1K ohm load, other 4 inputs grounded: 8mA, reducing to 6mA drawn when resistor is changed to reduce output frequency from 3.2MHz to 450KHz.
74AC14, schmitt hex inverter, 3 gate oscillator with one extra gate as a buffer, 1K load, 2 spare inputs grounded: 10mA at 3.2MHz
74HCU04, plain inverter, 3 gate osc with an extra gate as buffer, 1K load, 3.1MHz, 16mA, and much cleaner edges with less rining than any of the setups with the schmitt inverter (singly or in triple gate arrangement). Also found this drew 8mA if resistor varied to give 250KHz output, and 28mA if resistor made smaller to give 20MHz out. If the resistor was entirely removed so oscillation stopped (R ≈ "infinity" from the third gate's output to the first's input) then 5mA was still drawn, guess this is from putting current in to the 1K load at the buffering gate's output.
All types had the frequency vary somewhat if the suply voltage were canged, for example from 2.9Mhz at 4.6V to 3.15MHz at 5.3V.
Frequencies differed between the tests as I kept the same cap in place and just varied the timing controlling resistor to change frequency, picking whatever was closest to 3MHz from resistor values to hand, plus doing some slower and faster tests to get a feel for current consumption vs frequency.
So it seems the single gate inverter can be more efficient, and schmitt triple is more efficient than doing the triple with normal inverters, and any inverter gets more current hungry at higher frequencies. Still, the lack of ringing on the edges of the triple gate plain inverter version is pretty desirable, guess I'll be putting up with 16mA or so of current as the price of this over the schmitt inverter's ringing.