Ahoy! Thanks for stopping by… Hacklab sent you the right way ;)
I presume you’re looking at the Raspberry Pi 2 with Pibow Case? - http://shop.pimoroni.com/products/raspberry-pi-2-with-pibow
Basically, the Pi 2 is the way to go. While the case differs in form-factor, the Pi that you get inside is exactly the same.
Well done for spotting the difference in circuit components, by the way, those photos were taken over a period of time that includes the B+ and Pi 2, but the Pi you get is the newer, Pi 2. ( The case, however, is compatible with both )
I heartily recommend the Pi 2 in a Coupe case. It’s designed to be the case for people who will be tinkering with their Pi, so it keeps everything on the bottom protected but gives easy access to the GPIO pins on top- for using HATs, ribbon cables, etc.
The larger case ( which we just call Pibow ) is great for fully protecting a Pi that you plan to use as a desktop computer replacement, or just for programming. It doesn’t give such easy access to the GPIO but you can buy a replacement top which turns it into a Coupe: http://shop.pimoroni.com/products/pibow-modification-layers
Whatever you choose, you can’t go wrong with the Pi 2 & Pibow. But beware you’ll also need a power supply: http://shop.pimoroni.com/products/raspberry-pi-universal-power-supply
( You can use any Micro USB power supply you might have knocking about at home, but we find this often causes problems later with add-ons that need extra power )
And, unless they already have SD cards from elsewhere, the NOOBS SD card: http://shop.pimoroni.com/products/noobs-8gb-sd-card