I don't like to rely on their red for the buff because I like to ambush their jungler at Red at the last second to make sure I get the red kill and the jungler, and smite has a larger range for it.
I guess the difference is that I rarely expect to encounter the enemy jungler at their red, so my goal is to simply kill their red asap then gank. There are basically 4 scenarios that play out when I'm Nunu jungle:
Scenario #1: Normal Start, Enemy jungler goes blue then his red, I normally kill his red before he gets to it then I gank top or bot.
Scenario #2: Double Invade, both junglers start Blue, both junglers invade each other's red.
Scenario #3: Mind Games, Enemy jungler starts his red then does his own blue then goes for my red. (He assumes I will be invading his red 1st, which is true).
Scenario #4: Fuck Nunu, Enemy jungler starts his Blue, enemy support wards his red, team is ready to butt-fuck nunu.
Basically less than 25% chance I encounter the enemy at his red since most junglers have the mindset to counterjungle.
I encounter a lot of supports warding enemy red, it is very risky these days as a Nunu and in higher Gold divisions. What I do is look at the support's inventory and see if they've dropped a ward to know. Sometimes I'll abort and go straight for my red. I managed to catch a Jarvan last night invading my red, he started his Blue. I saw the support was missing a ward and decided to abort, I placed my ward in the bush behind my red and saw J4s flag pole go over Baron pit (I was purple side). He did manage to steal my red but we killed him for First Blood. I then went to his red which was still up, he was already respawned and attacking it. We killed him again, it was a 4v4 fight because mid/bot lanes converged from both teams but we won with 0 death. I took his red after the fight. So we started with 2 kills and J4 had 0 buffs and lost tons of xp. From then on we dominated and steamrolled to victory. The enemy ADC even said he was shocked at how bad they lost.