By anomalies I assume that you mean "cosmic anomaly that can be found with the onboard ship scanner." And empire space you mean high sec empire space.
Ratting in these anomalies may give you:
- Faction spawns
- Faction loot
- Expeditions / escalation
Faction spawns can sometimes give you special items or bigger bounties. Salvage from faction spawns may give T2 salvage.
Even without a faction spawn, you can get faction loot. Most common will be faction ammo (for example, 1000 rounds of shadow serpentis antimatter charges), but other types of faction loot are possible.
Sometimes, when an anomaly is cleared, you will get a message about an escalation that will send you off to another system that has another plex to run. These are very uncommon to find. Following the sequence may lead to very large rewards.
Clearing an anomaly such as a 'serpentis outpost' will lower your standing slightly with the serpentis faction (aggression and ship kill). It will improve your security standing. It will not help or hurt your empire faction standings.