The best examples that come to mind are when ordering food. As examples:
• You speak English and Spanish and are ordering a burrito
• You speak Thai and English and are ordering Tom Yum
I imagine it could depend on numerous things:
• You primary language or ethnicity
• What sort of restaurant
• Who you’re dining with
• Who you’re ordering from
• and probably a lot more…
Depends on how good I actually am at pronouncing the original version, how different the original version is from the current language and if I assume that my conversation partner is going to understand it. Also, I tend to have trouble with switching accents quickly. On the other hand, figuring out how to correctly butcher a pronounciation isn’t that easy if you’re not a native speaker of the butchering language.
I’m a native German living in Germany, English is generally fine, i.e. most Germans know English well enough that they aren’t going to be confused by a correct English pronounciation and my pronounciation isn’t that bad by German standards. Other languages can get dicey, though. TBH I tend to avoid pronouncing words that are neither German nor English and are hard to understand if you don’t know much about the language - e.g. “burrito” isn’t so different that Germans wouldn’t understand the Spanish pronounciation, but many French words are not very obvious if you don’t know French well, plus my pronounciation could be bad enough that it would even throw off native French speakers.
If I was in an anglophone country ordering German food, I’d probably pick the German pronounciation, because I’m not that good at guessing how anglophones in a specific area pronounce German words, and who knows how that would even come out if I try that with my German-accented English. But I’d expect that most of the servers don’t know any German and have trouble understanding me. I’d probably just say the numbers if it’s a numbered menu.