"what's better:
1 - higher iso but correct exposure, or
2 - lower iso but underexposure"
When I first discussed the topic of "exposing to the right" with Thomas Knoll several years ago, he made the point that exposure at the camera's native ISO (usually the lowest) and with desirable bright areas just below clipping, produces the cleanest results.
The rest is just amplification.
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That's a given, but that's not really a trade-off; it's an ideal situation.
The lowest ISO is only going to give less noise when it is fully exposed.
Unless you're shooting architecture with a tripod, there is often a set of unavoidable compromises. The trade-off between ISO and exposure varies with cameras, and different concerns apply to black noise and midtone and highlight noise (the former is affected mainly by readout and digitization processes, the latter by the literal sensor exposure in photons).
"Several years ago", there was a lot more gain-related readout noise than in current cameras. The recent Canons have readout noise at ISO 1600 that is already weaker than shot noise with exposures 9 stops below RAW saturation. If it weren't for the patterned line component of the noise, it would be even less visible.