Having said this, the joy of the Andsnes recording is that it is played on Grieg's piano in Grieg's own room so we capture a sound close to what Grieg originally heard. The best news is that Andsnes does play beautifully, even if I might have preferred some other tempos on occasion. By way of example, I much prefer Gilels sensitive, thoughtful and slow performance of Arietta. Still, I'm sure Grieg would say that Andsnes is closer to the way he conceived the music to be played.
If you are only to have one recording if Grieg's solo piano music (that's sad), then I don't think you'll regret purchasing the Gilels recording. If you don't drink the same wine with every meal, then consider this Andsnes recording. I think there is some delight in knowing whose piano is being played and where. I wonder what Grieg would say listening from a chair in a corner of the room?