I just looked up Square Cash, and it seems like it launched in 2015 according to Wikipedia. Everyone I know (who I would want to send money to/from) was already using Venmo by 2012, 2013 at the latest. I've yet to encounter a single instance where I wanted to switch, nor (anecdotally) have I heard someone voice a single complaint about Venmo in-person.
Venmo got to market with a pretty much pure product before anyone else, and has yet to give any cause for switching.
"In March 2015, Square introduced Square Cash for businesses, which includes the ability for individuals, organizations, and business owners to use a unique username to send and receive money, known as a $cashtag"
But for some reason they neglect to point out the pre-for-business component. It actually dates back to 2013:
https://squareup.com/news/introducing-cashtags
I stand corrected, though, because as you note, Venmo predates it by several years. I guess I just had no reason to switch from PayPal until Square Cash came along in 2013 and was even more frictionless. But ultimately, these things are clearly down to network effect.
Oddly, all I can find about the PayPal mobile app is that it was "re-designed" in 2013. Of course, I was using PayPal on a Palm handheld back in ~2000....
Venmo definitely won the first-to-market/network effect game. That said, I'm not complaining. Unless it looks like they are on course for bankruptcy or there is a major data leak, it's CX is pretty much exactly what I want it to be. The only unnecessary part is the social feed, but that has absolutely no impact on me unless I want it to (and sometimes it's amusing to see the messages my friends attach to them if I happen to look at it).
It looks like Venmo is ~2x as popular as Square Cash from this recode article:
https://www.recode.net/2018/2/27/17059182/square-cash-app-mo...
And a few other good data points/comparisons.
https://www.digitaltrends.com/mobile/paypal-vs-google-wallet...
https://lifehacker.com/money-transfer-showdown-square-cash-v...
(One source points out that Square Cash followed Square Wallet and Square Order; I used Square Wallet because I also had their card-reader from back in the day, so this goes back to at least 2011).