Understanding Proper Implementation Of Open-Collector
Both approaches will turn on the LED.

EDIT: note, however, that you will not be able to toggle the output using either approach because opening the switches does nothing to change the polarity of the input to the gates.

You may be confusing the polarity of the output. For open collector output logic gates the logic function is realized including the polarity inversion from the open collector.

So in your second example the NAND gate really behaves like a NAND at the collector output and the output is pulled low thus turning on the LED.