I wonder if using the wifi at a data center has the same broken browsing experience as using a VPN

From a datacenter IP, if the IP address is not shared with other users, you still get blocked from sites like Reddit, but you don't get most annoying captchas (for example on Google).

Yes and No. The internet sees it as a datacenter ip and some will degrade the experience based on that. Other are more strict and use a service like ipinfo.io (the op) to know exactly which Ip are used by a VPN provider and block access based on that list.