I don't know what you're talking about, Omega from XIV created several villains and characters from the franchise (including Exdeath) from places he visited, so yes, Omega from FFV is the same as all the games.
And omega also has conceptual manipulation for having created chaos, which is said to be a concept in itself, just like fighting Serah and Noel from FXIII who have type 1 conceptual destruction
The statements here are mostly true, especially the concept manip feats.
The story-related origins differ due to stylistic/narrative choices, but Omega has indeed crossed the Interdimensional Rift like in his other appearances. There’s also logs/statements of him having visited Kefka’s world (FF6) that backs it up— as well as creating an improved version of Chaos and Exdeath with footage. We also know that XIV Omega possesses ‘battle data’ from across the classic era of final fantasy titles— including data of his FF5 counterpart. He also sources data from FF5 (Bartz' World) in the form of manifesting settings from that title, alongside FF6's settings (the entirety of Sigmascape, which outright states "World of Ruin", and implies he has traveled to it in some cutscenes) within the Rift.
The abilities are the same, but to a much greater extent (it’s still 2-A tiering if we’re going off of Stormblood scaling here). The circumstances and origins, not so much.
Despite all of this, It’s also consistently hinted that the several Omega(s) are the same entity/ shades of the original Omega (FFV) across the games he appears in, and possess the ability to travel the Rift to some extent. In XIV in particular, Omega was specifically created by the Omnicron to destroy Midgardsormr during the war between Machine & Dragon— who’s myth also gave rise to the primal Shinryu in Stormblood at Baelsar’s Wall. He still possesses all of FFV Omega's abilities, which is essentially a blueprint for other iterations across the series; with the exception of a lone few (Omega Weapon from FF6).
(Tangentially relevant due to both Shinryu and Omega appearing together in the games they show up in— and they have been the antithesis to one another since FFV. All of their appearances are as twin Super Bosses. Shinryu is a similar case as well, although later on he's more relevant in the story and quite possibly scales higher.)
From what I’ve gleaned, the only noticable differences/additions for XIV Omega are:
EE, Environmental Destruction, Pocket Reality Manipulation, and Concept Manipulation (types 1, 2, and 3), BFR (Another layer of it separate from Encircle, alongside nearly killing the WoL on two separate outside of raid instances + being able to BFR people to the void. The first requiring Midgardsormr's Intervention, then Alpha's.), and Creation
within the Rift— alongside Data Manipulation, Info Analysis, and Barrier Creation (with Omeguard, which applies to base Omega), Flight (suggested in FF5, seen in FF14), Black Hole Creation (After the Years via Black Hole), Fire Manipulation (After the Years via Meltdown) and several of the Raid Mechanics from O11N that are subjectively already listed under ability, just not moveset/arsenal. The most powerful of the additions for XIV Omega would also be his stupid Adaptive Evo hax
within the Rift. (I may have missed some other things)
( Edit: He also creates
Alpha too, I guess. )
As for his profile, I wouldn’t be opposed to three new keys: Base (
Matching Shinryu in power), O11N (Far greater in the Interdimensional Rift), and O12N (Higher than before) respectively for his XIV Iteration— it just seems like he’ll get buffed in the end. Alongside additions for other missing things from base Omega.
And for simplicity’s sake and the most logical conclusion— both Omega and Shinryu should have assumed their base forms in their first fight in Stormblood. Omega was nowhere near as strong in their first encounter (and also took place at Baelsar's Wall)— not until we see what he’s capable of within the Interdimensional Rift in XIV— since he was able to explicitly control, create, and destroy reality within the Rift and has been constantly referred to as a “Master of the Rift” in Omegascape + raid summary material/scans... in addition to being capable to traveling across shards and to the world of other games through it.
BREATHES (I promise this isn't flowery language, it's actually stupid and a lot to dive into. Especially with the hundreds of hours of Endwalker dumping a treasure trove of information on Omega + an entire beast tribe questline that involves them.)
Dare I say that XIV Warrior of Light should also scale to XIV Omega for Stormblood, rather than Neo Exdeath (reason being that savage content isn't treated as canon, and Omega scales higher than him anyways. It's technically a buff higher into 2-A. ) for his Post-Stormblood key. There's a few things to consider that may have ramifications like these, and could turn into a much bigger CRT.