left side: each led is limited to a particular current by its own resistor ... ex each led is limited to 10mA , then total current is 10x8 = 80mA.
right side: all leds are limited to a current value set by the resistor.... ex r9 limits the current to 20mA, then each led gets more or less 20mA / 8 = 2.5 mA . More or less because some leds will draw a bit more current, others will draw less.
Also note that if one led burns out/gets damaged, the rest of the leds will share the same current, for example 20mA / 7 = 2.85mA. If you're unlucky, 1-2 faulty leds can cause a cascade and burn all the leds.
=> the left version is preferred.
note that a lot of shift registers can only do about 25-50mA so you might want to use npn transistors at the outputs of the shift register (with a suitable small value resistor between output and npn base) and get the current from another input, don't power the leds straight from the shift register if you want them to be bright.