Following this post, I was able to get Nextcloud running with a LAMP stack on Ubuntu 20.04.
I had to make a few tweaks to fit the configuration to my environment. Even though I am running it on a low-powered box, it has no trouble with concurrent uploads/downloads. The bottleneck is the network as expected.
The mobile UI is faster than the desktop however my cellphone connection is weaker, hence the slower upload speed. Finding what you are looking for is intuitive and everything works as expected.
With a normal connection speed, uploads proceeded at the expected rate.
My initial impressions of Nextcloud are positive and I would recommend it for a homelab or potentially a backup/special use case system in an enterprise environment. It is useful for simple file transfers and the collaboration tools seem promising. https configuration using Letsencrypt is simple and provides sufficient privacy.