The first is pretty good, and his analyses late in the video on ring true. The second has some clearly correct things, but implies some incorrect things, and so ends up being confusing.
The confusion in the second is from incorporating a particular perspective from the apparent contradiction of predestination vs. free will. The problem is that there is no actual contradiction, which isn't clear in the logic of the second video.
Without going into the whole mountain-sized issue of predestination vs. free will, I will just point out that the parable itself addresses the verse in question.
The verse being examined is:
“For many are called, but few are chosen.” (Matthew 22:14, 1995 NASB)
And the question is, who does the chosen refer to?
The answer IMO, is found in this (and other) verses:
And he sent out his slaves to call those who had been invited to the wedding feast, and they were unwilling to come. (Matthew 22:3, 1995 NASB)
The chosen are the ones who were willing to come, rather those who were unwilling to come. In this passage, who God chose is the same as the group of people who chose to come.