English Translation
I beg to differ, as I disagree with your analysis of the situation.
The JP/EG doesn’t match.
- 君と違ってその状況分析には賛成できないよ。= Unlike you, I don’t agree on the analysis of the situation.
- I beg to differ, as I disagree with your analysis of the situation. = 失礼ながら、あなたの状況分析には賛同しかねます。
The first pair means that the analysis was proposed by a third person. You (the listener) and I (the speaker) have different opinion on it. There is no nuance of “beg to”. The way of talking is pretty straightforward.
The second pair means that the analysis was submitted by you (the listener), then I (the speaker) disagree “with all due respect”. 賛同しかねます is a politer yet still determined way to disagree. You can replace 失礼ながら (due respect) with 誠に失礼ながら (with all due respect) or 残念ながら (sorry to tell you that).