Crystal oscillators tend to age down in frequency due to outgassing. The outgassing contaminates the quartz plate surface and add mass, thereby reducing frequency. Outgassing increases with temperature so all else being equal, two identical crystals, one in an oven and one at room temperature, the oven crystal will age downward faster than one at room temperature.
However, crystal oscillator manufacturers are aware of this problem and a high precision oven oscillator will have a crystal in a hermetically sealed enclosure, possibly vacuum or at least dry nitrogen. But, they still tend to age down in frequency as it's impossible to have the crystal holder perfectly free of contaminating particles and sealed.
On the other hand taking a run of the mill el cheapo microcontroller crystal and running it at 85 deg C in an oven will quickly drive it down in frequency.
A good oven oscillator will age slower with operating time, with a good percentage of long term drift occurring in the first few thousand hours of operation.