My inexpert ear tells me that I can barely tell what guitar is on a record beyond, generically, it's a Gibbo/Strat/Tel/other. I can't say that I can tell what name is on the headstock just by listening.
A somewhat facile argument but just to get across that your listeners will not know the difference and the name on the headstock only matters when people can see it. One of those is the prospective owner, of course and it may matter greatly to them. Consider this if you are buying it as a present for someone, who may be brand-conscious.
Lastly, there was a notorious period of poor quality control in US-made units, after a takeover. Some far-east built Squiers are considered better built, hence the answer to your question is not an unequivocal "non-Squier is better".
So, get them to try both *using an amp similar to what they own* and buy either on 'best feel' or on what the wallet dictates.