There is a myth that Robespierre was guillotined faced-up (he wasn't); but it raises the question of which aristocrats or disgraced revolutionaries were provably guillotined face-up during the period of the French Revolution (1789 - 1799).
Cursory googling suggests they were always face down during the French Revolution.
According to legend, he was placed face up in the guillotine (prisoners were typically placed down).
But then, he - and other internet references I ran into - throws in a "typically" just in case, and offers no sources or references in the page notes to support the assertion.
This much I would suggest, though. A legend holds that Robespierre was placed face up and it would have been unusual and crazy enough that the legend lives on to this day. Seeing that there are no such legends about other people, methinks it's reasonable to assume it seldom if ever occurred during the French Revolution - else for sure you'd also hear about this or that other legendary person who lost their head face up, either as an act of added cruelty or bravery.
(In passing, one runs into other web pages that suggest that the Nazis were using guillotines face up, for the added cruelty.)
[in 19th century Germany]... victim being decapitated either face up or down depending on how the executioner predicted they would react to the sight of the machine
The strongest support for aristocrats being guillotined face-up comes from the joke:
A commoner, an aristocrat, and a scholar (or engineer - but not a scientist! the word "scientist" came around in 19th century) are about to be guillotined. The executioner asks for their preferences, and the commoner says: "face down, I am too scared". He is placed face down, the knife falls down and gets stuck, and the lucky commoner is released - one cannot be executed twice.
The next is the aristocrat, and he says, that, as a warrior, he has always faced death without fear and he wants face up. He is obliged, the knife gets stuck and he is released.
The scholar says that his curiosity requires him to see everything, so face up he goes. The knife falls down, gets stuck, and the scholar screams: "there, I see it, I know why it gets stuck!"
PS. I am only adding the answer to be able to tell the joke ;-)
PPS. Common sense militates against the possibility of the alternative existing. IOW, each specific device is probably optimized for either face-up or face-down placement because of the anatomical front vs back differences.