I think it depends on the context. In those examples, there's not much to go on. I agree that it's not very clear which is supposed to be better.
I personally would think that IF one weighs more than the other (which I don't think there's a clear cut answer for), "nice" would generally be on top slightly.
Example of nice sounding "better" than good:
- That's a nice car.
- That's a good car.
"Nice" gives me the impression that the car is exceptional, while "good" gives the impression that the car is simply solid or reliable, or maybe just acceptable.
However, sometimes nice means "quaint" while good means "excellent".
- That was a good movie.
- That was a nice movie.
To me, "good" now has more weight — it's almost the exact opposite. "Good" means the movie was very enjoyable (would watch again), while "nice" means it was only fairly enjoyable (might not watch again).
This is of course just my personal interpretation.
Conclusion: Good question. Of course, the meaning is quite different when we talk about people (Good may mean "does good deeds", while nice may mean "pleasant"). You can be evil and nice at the same time. However, I think in the context you put it the meaning is quite ambiguous. "Good Answer" and "Great Answer" would be much clearer.