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You gain low latency, which allows you to write your code to a 'pure' relational model (at least as close as SQL allows), without having to rely on code complicating hacks to deal with round-trip issues. Less complicated code can improve delivery time and reduce faults. While there are abstractions that can be used to help with those hacks, they come with their own tradeoffs. Pick your poison, as always.

Conceptually, RDS is little more than SQLite with a clever networking layer built on top. In context, your application is also just a clever networking layer, so the middleman doesn't necessarily add any value. Of course it depends on exactly what you are trying to do and what tradeoffs you are willing to accept. There is no free lunch.