I ran the same complex (but still simplified) version of one our real world queries with both the Relay API turned on and off. The relay response is almost 2.5x slower.

The only difference was at the very at the very start of the query to handle the relay structure

query MyQuery {
  accounts_connection(where: {id: {_eq: 496}}) {
    edges {
      node {
        id

vs

query MyQuery {
  accounts(where: {id: {_eq: 496}}) {
        id

And the rest was identical.