In what ways does Enemy Within alter the base skills from XCOM:Enemy Unknown?

Solution 1:

Close & Personal: Totally new skill by the same name as the old. "The first standard shot made within 4 tiles of the target does not cost an action". With that skill you will see an orange circle around each enemy. The soldier can enter that circle, shoot at the enemy, and then either take the second move or shoot again, this time also at another target. This skill cannot be combined with Run & Gun. After a standard shot within the orange circle, the second shot can be Rapid Fire, for a total of three shots in the turn. If Rapid Fire is used on the first shot, the turn will end.

HEAT Ammo: The damage increase against robotic enemies has been reduced from 100% to 50%.
Grenadier: In addition to allowing two grenades to be carried per inventory slot, this now gives frag, alien and needle grenades a +1 damage bonus.

Headshot: The extra damage done by Headshot now depends on the sniper's rank rather than the tech level of their weapon.
Squad Sight: Shots with squad sight can no longer crit, unless Headshot is used.
Snap Shot: Offensive Penalty reduced to -10 from -20.

Covering Fire: Now triggers before the overwatch target attacks, rather than after.
Smoke & Mirrors: Now gives two extra smoke grenades rather than one.
Deep Pockets: Deep pockets no longer gives an additional inventory slot. Instead, limited-used items carried by that squad member (such as medkits) get one more use than they otherwise would. By the way: A second inventory slot can now be unlocked for all soldiers with the Foundry project Tactical Rigging.