@Lina98 the Kristeller system is not actually a speculum. There are 2 separate valves, one to pull upwards, the other downwards. This system is rather used when it is necessary to perform an surgical procedure to open the vagina more widely. In this practice, it is most often the assistant who holds the upper valve, rarely the patient.
Concerning the model used, it is indeed the doctor's practice which makes him prefer this or that reference. We also tend to keep habits learned during studies, personally I'm more Collin.
As for the plastic or metal debate, for some it is an economic question.
In several regions of Europe, the doctor asks the patient to buy her speculum in a pharmacy before the consultation, so plastic models are used and then thrown away (bad for the carbon footprint)
In France some have done it but it is against the rules of the Health Insurance Fund. The consultation with the gynecologist is reimbursed but it is up to the doctor to provide the equipment he uses. The disposable system is therefore much more expensive than re-sterilized stainless steel instruments.
The argument that they are colder is not true; many pedestal tables are equipped with drawers allowing them to be brought to the correct temperature.
I find that the plastic models are less easy to introduce because they stick a little, however I think that you should always have some in advance in case you suspect a resistant infection (hepatitis C for example see HIV)
Concerning the size of the valves, it is the art of the gynecologist to have an eye to know which one will best correspond to the anatomy of his patient. To answer @bedwetter_bobby No, we do not do the bi-manual touch before because this would pollute the samples that we have to take during the smear once the speculum is in place.