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LC tank circuits have a much wider bandwidth ( read lower Q=100typ vs. XTAL Q=10k) less stability,and thus more phase noise, more temperature drift, sometimes more cost.
However power dissipation in crystals is limited to 100uW which is much lower than tank circuits. Tank circuits can operate at much lower frequency although at greater expense special crystal cuts can be achieved in the VLF range.
For higher than 50MHz, the choice swings from Crystal harmonics to SAW resonators.
So it becomes a specific requirement for resonator power or stability requirements over cost.
People who buy Crystal Oscillators (XO) vs make them may have unique reasons with less than adequate documentation control and source control of crystal purchases to meet stability specs.
Crystals in volume are under 25 cents. TCXO's with 1ppm stability over wide temp. are now $1. ( which once was $50)
To my knowledge, crystals are used in situations where high frequency precision is required.
Old radio stations used to have an issue where over time their frequency would drift off, but with crystals this issue was addressed.
Other than that, all of these have resonant properties, though some, such as a tank circuit, may be better suited for higher loads.
LC tank circuits have a much wider bandwidth ( read lower Q=100typ vs. XTAL Q=10k) less stability,and thus more phase noise, more temperature drift, sometimes more cost
Lets get this right, "tank" circuits are the LC circuits in a class B or C RF amplifier, where the the missing half cycles are supplied by the energy circulating in the TANK CIRCUIT. The term has become wrongly associated with any low level LC resonant circuit.
So lets presume the question is how do LC and crystal oscillators compare.
Crystals :- high stability (F +- .00001% per deg C*), tight tolerance( +- 100 HZ), cannot be adjusted very far in frequency (+- .1%?)
LC low stability ( F +_ .1 % per deg C*), wide tolerance (+- 5%?) can be adjusted easily (+- 50%)
* uncompensated
Cost /size dependent on tolerance and stability and quantity.
Frank
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