Let's make a minimalist assumption - plain vanilla '51.
Parallel variant: memory-mapped 74xx573-like latches.

LoadLED:
      mov   dptr,#MemoryAddress
      mov   p2,#HIGH(LatchAddress)
      mov   r0,#LOW(LatchAddress)
      mov   r2,#LatchesCount
Loop: 
      movx  a,@dptr      ;2 cycles
      inc   dptr         ;1 cycle
      movx  @r0,a        ;2 cycles
      inc   r0           ;1 cycle
      djnz  r2,Loop      ;2 cycles  = 8 cycles per loop

Serial variant: a chain of 74xx595 connected to RxD/TxD, UART in mode 0 (SPI-like).

LoadLED:
      mov   dptr,#MemoryAddress
      mov   r2,#LatchesCount
      clr   LatchPin
Loop: 
      movx  a,@dptr      ;2 cycles
      inc   dptr         ;1 cycle
      mov   sbuf,a       ;1 cycle
      nop                ;1 cycle
      nop                ;1 cycle
      nop                ;1 cycle
      nop                ;1 cycle
      djnz  r2,Loop      ;2 cycles = 10 cycles per loop
      setb  LatchPin

Where is your significant speedup with the parallel solution?

Moreover, Erik suggested you to load 8 serial lines simultaneously, then there is no overhead.

And, I would never do a 1:32 multiplex unless the datasheet for your LEDs claim they can be pulsed with a 32x nominal current; otherwise your overall brightness will be low.

Jan Waclawek