07 suburban 5.3 to LS3 6.2??

I don't have experience with anything past LS2, but I suspect your 07 ECM would only need a tune to run an LS3. This assumes your 07 is drive-by-wire.
Perhaps someone at ls1tech could give you more details.

While the LS3 is undeniably nice, it will likely cost twice as much as a 6.0 LS2 and three times as much as a 5.7 LS1. Used LS3 are very rare unless you have a lucky connection.

 

I drove a 2008 Denali 4WD with the 6.2L Vortec.
I wasn't all that impressed to be honest to go out of my way for one.

Didn't have as much acceleration as I had anticipated at all.
Felt about the same as the 5.3L to me in my cousin's Tahoe.

I think the LS3 wouldn't have as much torque down low due to the car intake on it.

 

As mentioned above, both your 2007 5.3 (I assume LY5) and LS3 are Gen IV engines. As such, the ECU you have will work on the LS3 after flashing it with the appropriate tune.

 

my DD is an 04 Suburban 5.3 AWD, and, while not a racecar, I would not describe it as slow - perhaps I'm geared lower than average but the thing pulls like a freight train

 

I'd get somebody local that uses HP Tuners to do a good tune and wake it up. Money well spent