IIT

I think IITs are a bigger brand than IIMs, atleast outside India.I can only think of the following reasons :
After undergraduate studies from IITs (for which they are known), the students have options to venture into diverse fields, from management to government services, from entrepreneurship to PHDs. Thus they have wider impact on the society, and better brand name.
Most of the students in IIMs have already decided their career paths, and go for relatively similar careers, thus affecting mostly corporate sector.
IITians have contributed a lot to technology sector of the west, and it has been acknowledged there. This is mainly because most countries encourage the "import" of engineers but not managers. IIM grads may have contributed to Indian economy, but it hasn't been acknowledged that much.
IIT's are far bigger than IIMs. IIT Kgp alone is bigger than all the IIMs (including the new ones) combined. Thus they have richer alumni network, and a bigger brand.