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Design
A Hartley oscillator amplifies the electronic resonance of a pair of coils in parallel with a capacitor to produce radio frequency oscillations. A crystal oscillator also uses coils and a capacitor, but only to set a crystal into resonance. You can make simple, single-transistor circuits for both kinds of oscillator.
Frequency Stability
Quartz crystals resonate at specific frequencies. Crystal oscillators use this resonance to govern the frequency of the circuit, and it stays accurate to a fraction of a percent over time. The frequency of a Hartley oscillator depends on the values of the coils and capacitor, both of which drift with time and temperature.
Tunability
The stability of a simple crystal oscillator also means it's fixed at a single frequency. To tune it, you must switch in different crystals or resort to complex methods such as frequency synthesis. You can easily tune a Hartley oscillator by using a variable air-plate capacitor, as was done in older radios.