in Normal you can easily skip right passed lasers

in Classic you cant afford to wait

All enemies except Sectoids have ramped up health and accuracy - you need them dead NOW - and your soldiers have reduced accuracy bullet weapons just wont cut it after the first month

Similarly in Normal you never need to use anything but light plasma rifles (for the +10 aim buff) but in classic as soon as the trooper has leveled enough not to need the bonus (captain and up in my experience) they should swap to a full plasma rifle for the extra damage (elite mutons have 14 health and come in groups of 2 or 3)

From my own experience Normal is cake walk - Classic is a true challange