It is my understanding that obligate asexual organisms are generally less adaptable to new environments. While they may have new mutations, if there is no gene transfer (conjugation in bacteria, sexual reproduction, etc) then new mutations never have the opportunity to get shuffled and recombined into potentially useful combinations.
So, I would expect parthenogenic organisms to be fit for their environment, but genetically less able to cope with change.
Comparing 2 hypothetical broods of \the same species in a sort of thought experiment. Assuming a carrying capacity of some very small number of organisms (let's say 2, to be extreme) and assuming that genders are a non issue (so the species is not tragically doomed if two of the same gender are in the same generation). Finally, assume that each population was founded by a single gravid female.
100 generations later:
The gene pool of the parthenogenic species should be essentially identical to the founding female. No significant loss or gain of genetic information (ignoring the small rate of mutation)
The gene pool of the sexual species will be greatly degraded, as each generation will lose some measurable amount of genetic info (imagine a family with 2 children- is EVERY gene present in each of the parents present in the children generation- NO). You would be left with a very homozygous population. While selective pressure could/would have generally preserved the positive traits, in such a small population random chance events could remove a positive gene from the population at regular intervals.
So, back to the initial posting...
If one had to start a colony with a single gravid female, a parthenogenic species should not have significant genetic impacts from that. If one had to start with a single gravid female of a sexual species, it would be on utmost importance to keep as many of the first few generations of individuals alive as possible to preserve all of the genetic variability of the mother, and to maintain the colony at a level where statistically each of the genes (all of the variation) would be present in various individuals of each generation. What that magically number of individuals is, I have no idea, but for myself, I would err on the side of more offspring, at least in the first several generations.
Speaking entirely theoretically...