There are substantial differences.

For one, as non-root user you are tied to the permissions system and can't access most of the data. If one of your services (let's say sql) get hacked, they are tied to sql user, and unless the achieve privilege escalation, they can't mangle with other services data (eg webserver).

Also network wide, a non-root user can't use different protocol than tcp and udp. The only reason you can ping as a regular user is because of the setuid on the ping program, otherwise icmp is not allowed to non-root users.

There are of course other reasons, but these are some examples on how it would be different.