What are the differences between normal and classic difficulties?

Solution 1:

You can find a detailed overview of the differences between all four difficulties in this thread on the 2K forums.

Here is what that thread says about Normal and Classic:

Normal:

1. Base global panic starts at 0
2. Most minor alien activity raises panic by 1 in left unchecked with some events doing up to 3
3. Your soldiers have no bonus hitpoints
4. Aliens have their AI mostly unshackled
5. Soldiers cost $10

Classic:

1. Base global panic starts at 8 (1 per location)
2. If unchecked alien activity causes at least 1 panic, but will often cause 2 or 3
3. Your soldiers have -1 hitpoint
4. All aliens receive bonuses hit hitpoints, accuracy, critical change and / or damage.
5. Alien AI is unshackled
6. You don't receive officer training school for free. You must unlock and purchase it.
7. There are even more aliens per map
8. Soldiers cost $15

Solution 2:

Other differences

Normal

• you start with 37 energy in your base
• satellites cost 100 to begin with
• you may have more open spots for construction in the base

Classic

• you start with 30 energy in your base
• satellites cost 100

Solution 3:

My answer is based on reading impressions/ my impressions (mind, my own classic mode game is barely started), and this interview:

1. On the strategic layer, aliens expand more quickly. The panic meter will increase more rapidly. Mission rewards will be smaller.

2. In battles, aliens have better AI and some will have more health. They will do a better job of making use of abilities and more aliens will attack at once (as opposed to coming in smaller groups in normal, e.g.). The interview talks about how Thin Men get an extra health point to make them grenade proof, but floaters did not get extra health. Apparently morale will be more severe in battles as well, which means more panics when things go bad (as they invariably will).