Are you to going to do stuff in Nagoya? (which might determine your choice) Or is it a transit point?

For transit, I would choose the Sofitel - very close to Nagoya station, whereas the Westin is a long way. Also, the Westin looks dangerously like a rebranded 1970s Japanese hotel. (I suppose the Sofitel might be too...)

I know that you avoid taxis, so perhaps you have worked out the cheap route to the Westin... For myself, I would be calculating a few thousand yen for taxis between Westin and station, which would shrink the price difference somewhat.

And are the only choices those two?