What additional information does show ip interface provide compared to show ip interface brief?

It adds detailed IPv4 protocol settings the brief view omits — broadcast address, MTU, helper address, applied ACLs, Proxy ARP, and ICMP redirect behavior (and show ipv6 interface shows link-local/global addresses, multicast groups and ND/DAD).

show ip interface Command:

Provides detailed IPv4 configuration for an interface.

R1# show ip interface g0/0/0
GigabitEthernet0/0/0 is up, line protocol is up
  Internet address is 192.168.10.1/24
  Broadcast address is 255.255.255.255
  Address determined by setup command
  MTU is 1500 bytes
  Helper address is not set
  Directed broadcast forwarding is disabled
  Outgoing Common access list is not set
  Inbound Common access list is not set
  Proxy ARP is enabled
  Security level is default
  Split horizon is enabled
  ICMP redirects are always sent

show ipv6 interface provides:

• Link-local address (FE80::...)
• Global unicast addresses
• Joined multicast groups (FF02::1, etc.)
• MTU size
• ND (Neighbor Discovery) settings
• DAD (Duplicate Address Detection) settings

Go deeper:

• IPv6 — addressing and Neighbor Discovery (Wikipedia) — link-local/global addresses, multicast groups and ND/DAD that show ipv6 interface reports.
• Cisco IOS (Wikipedia) — the verbose show ip interface detail vs. the one-line brief view.