2.8 gear inches isn't a huge amount, and the weight and stiffness of the new bike may offset that. However, if you're really struggling now, then that may be enough of a difference to make your ride miserable. OTOH, if you have a better time riding without shifting constantly, then maybe that will encourage you to ride those hills more, and your fitness will improve fast. Not wasting any time getting your momentum up downhill and not shedding momentum too fast by having to shift so much couldn't hurt either on hills of that length.