Crystal in temperature controlled environment vs OCXO
Only temperature is actively controlled. Usually OCXO and XO (and TCXO) units are hermetically sealed so humidity is not a factor. 

All oscillators and crystals are designed to have little effect from barometric pressure changes and forces on the leads. 

Edit:
@Enerwal makes a good point about the crystal cut. Apparently SC ("stress compensated") cut crystals are most used for OCXOs, as well as IT cut. Here is a comparison of the SC cut against the AT cut more commonly used for non-ovenized oscillators. From this source is a comparison of the temperature sensitivities (graph below) but there are other important differences such as aging and drive sensitivity and pressure sensitivity.

 

They appear to be better in many regards, but have an unwanted oscillation mode that needs to be suppressed by the circuitry, require vacuum in the cavity and are generally more fussy and labor intensive to produce, thus more expensive. They are less pullable (higher Q), which means they have to be trimmed to a tighter tolerance. 

Of course aging is accentuated in OCXOs that have an high internal operating temperature.