"Since they have the same sized wheel, you can neglect that in your calculations. So, the 44/16 gives you a ratio of 2.75, and the 42/14 has a ratio of 3.0. So, the new bike should be harder."

dont forget, wider tires typically have significantly higher profile. Theyre most probably NOT the same wheel size. Having said that, there's no way that the profile dif between the two will acount for the 6-or-so gear inch difference.