Does it make a difference if I buy a console version of AC4 2nd hand? Is there anything you get when you buy it new that I won't get if I buy it 2nd hand?
Every copy of Assassin's Creed IV: Black Flag comes with a Uplay Passport, giving you access to the Uplay store, which is used to redeem Uplay rewards that can be used in singleplayer or multiplayer mode.
Redeeming the Uplay Passport also gives you access to some of the multiplayer features, such as the ability crafting system, which is available after reaching Prestige level 1.
Every copy of the PS3 version of the game also comes with a voucher that'll allow you to purchase the downloadable PS4 version of the game at a reduced price. That particular voucher has a limited validity, however. In order to play the PS4 version, you'll have to keep the PS3 version of the game disc in your PS4's drive.
The Xbox 360 might have a similar voucher; feel free to edit this answer, should you know more about it.
Exclusively for the PS3 version (possibly also the future PS4 one), there is the Aveline mission DLC.
There is always a chance, that the previous owner didn't redeem one or several of these items, although you shouldn't exactly count on it.
In case your second hand copy is missing any of these: both Uplay Passport and Aveline DLC can be purchased separately. The voucher, however, can only be obtained if not already redeemed by a previous owner.