Version Exclusive Pokémon in Omega Ruby:
(Does not include Legendary Pokémon in the initial list, which is what you asked for.)
Kabuto (Fossil is only available in this game but Pokémon receivable if the fossil is traded over.)
Kabutops (Fossil is only available in this game but Pokémon receivable if the fossil is traded over.)
Seedot
Nuzleaf
Shiftry
Mawile
Zangoose
Solrock
Shieldon (Fossil is only available in this game but Pokémon receivable if the fossil is traded over.)
Bastiodon (Fossil is only available in this game but Pokémon receivable if the fossil is traded over.)
Throh
Archen (Fossil is only available in this game but Pokémon receivable if the fossil is traded over.)
Archeops (Fossil is only available in this game but Pokémon receivable if the fossil is traded over.)
Skrelp
Dragalge
Version Exclusive Pokémon in Alpha Sapphire:
(Does not include Legendary Pokémon in the initial list, which is what you asked for.)
Omanyte (Fossil is only available in this game but Pokémon receivable if the fossil is traded over.)
Omastar (Fossil is only available in this game but Pokémon receivable if the fossil is traded over.)
Lotad
Lombre
Ludicolo
Sableye
Seviper
Lunatone
Cranidos (Fossil is only available in this game but Pokémon receivable if the fossil is traded over.)
Rampardos (Fossil is only available in this game but Pokémon receivable if the fossil is traded over.)
Sawk
Tirtouga (Fossil is only available in this game but Pokémon receivable if the fossil is traded over.)
Carracosta (Fossil is only available in this game but Pokémon receivable if the fossil is traded over.)
Clauncher
Clawitzer
Version Exclusive Legendary Pokémon in Omega Ruby and Alpha Sapphire comparison:
Omega Ruby: Ho-Oh, Groudon, Palkia, Tornadus and Reshiram.
Alpha Sapphire: Lugia, Kyogre, Dialga, Thundurus and Zekrom.
Source