Find out which sleep mode your Mac uses

You should use Terminal to find out which sleep mode your Mac is currently set to use. Then you can use Terminal to change it to a different mode if you want to.

pmset -g | grep hibernatemode

Possible results are:

hibernatemode 0 (standard sleep)
hibernatemode 1 (hibernate mode, for pre-2005 portable MacBooks)
hibernatemode 3 (safe sleep)
hibernatemode 25 (hibernate mode for post-2005 MacBooks)

Changing is possible executing following command:

sudo pmset -a hibernatemode X

Sleep modes are explained in more details here.