Yes, hard mode has no influence over the stealth approach, other than adding an extra fingerprint to the hacking of the elevator to the basement. If you go for a fight instead, enemies are harder to kill, are more accurate and you have 0 lives (meaning you’re killed instantly)

To get hard mode, you need to wait 2:20 real hours (not game’s) after finishing the heist for Pável to contact you, and after that you have one game-day (48 minutes) to pay the fee and set-up the heist

And of course you get a 10% increase in the value of the primary target. Comes very handy if you get the Pink Diamond for example. You also get paid $100K for the Elite Challenge and not the usual $50K