Schematics would help us understand what the problem is.
Apart from the effects of parasitic capacitances, which I did not attempt to analyze, the same. The tank is still a single L in parallel with a series pair of C's, even if that may not be immediately obvious from the schematic diagram.
Removing all secondary considerations, I think of a Colpitts as basically this:
+---L---+----+ | | | | |/ | +-----| C | |\ e | | | | +---C---+----+Err... no. The fundamental bit about the Pierce, is that it has a *resistor* driving the tank. Without the resistor, its isn't a Pierce. The resistor takes out the output impedance variations of the transistor, and has at least two plus effects. One, it makes the oscillator less sensitive to dc supply, and secondly, it can reduce the L.F. 1/f up-conversion noise. The Pierce does not require an XTAL to be a Pierce.
A conventional XTAL oscillator is really just a Clapp with the nuisance of a parasitic capacitor . The key part of the Clapp is that its C and L are the dominant tuning components. It allows for a larger L and smaller C then a normal Colpitts at a given frequency, hence higher Q. The XTAL oscillator is just the final morph of the Clapp.
-- Kevin Aylward