As a test, I wrote down in English what I thought each reply said, and let Google translate it:
First question
Yes, GPT can write correct Latin. I am a large, open language model trained to write and respond to questions in Latin and other languages. However, as in all areas, it can happen that I won't always write accurately and without errors, especially in cases where the question is not sufficiently clear, or where I don't have the latest information.
Ita, GPT recte Latine scribere potest. Sum magna et aperta exemplar linguae Latinae et aliis linguis ad scribendum et respondendo eruditum. Sed, ut in omnibus locis, fieri potest ut non semper accurate et sine erroribus scribam, praesertim in casu ubi quaestio non satis clara est, aut ubi novissimas notas non habeo.
Observations:
- Google doesn't parrot the incorrect recto from the question and writes recte.
- Google translates “model” as exemplar, which is at least better than not translating it at all, I guess. It is difficult to say how this technical term should be translated, perhaps simulacrum?
- But then unfortunately proceeds to misgender the word exemplar.
- I don't even know what to say about linguae Latinae et aliis linguis ad scribendum et respondendo eruditum. I thought surely Google would at least beat the trainwreck at the beginning of the GPT answer, but not really.
- in casu ubi is Latinglish, that's not how you say “in cases where” in Latin. GPT's in casibus has the same problem.
- nota, -ae, f for “information” seems a poor choice, it means something like sign, letter. (GPT's informatio is also not correct.)
Second question
Saint Wenceslaus (Czech: Václav) was a ruler of Bohemia in the tenth century. He is said to have been a moderate and just king who loved his people and was dear to them. Legends also report that he faithfully pursued the Christian religion and converted his people to the faith. Regarding the precise way in which he ruled, the history is not very clear, however.
Sanctus Wenceslaus (Czech: Václav) erat princeps Bohemiae saeculo decimo. Rex moderatus et iustus fertur, qui suos amavit et illis carus fuit. Fabulae quoque referunt se fideliter Christianam religionem persecutum ac suos ad fidem convertisse. Quoad modum praecise quo rexit, historia non satis clara est.
Observations:
- “Czech” was not translated.
- Google uses the NcI for “is said to have been,” which is generally better, but note that the AcI with dicitur is occasionally found in classical Latin too.
- Actually it is more of an NsI because the infinitive fuisse is missing, which I think is not correct.
- qui amavit etc., Google and GPT both use an indicative relative clause in indirect speech, which is wrong.
- suos amavit sounds like he loved his family, suum populum is definitely clearer.
- illis should probaby be eis (similar to how GPT does it), because they were just mentioned.
- Google uses se in indirect speech to refer to someone who is not the subject of the main clause, which is wrong.
- Again with the missing infinitive, but in this case the missing esse seems more excusable to me.
- quoad + acc. for “regarding” is extremely unusual and doubtful.
- praecise is wrong, it says “the way in which he ruled accurately.”
In summary, I would say both are pretty rough, and I do not get the impression that GPT is significantly better than Google, but it is also certainly not significantly worse.