Omega is definitely better than Pyrrha is. Pyrrha is, IMO, somewhere along the lines of mid/upper-mid tier, whilst Omega is debatably top 5.
Pyrrha is better than Omega is a few regards, of course. She has slightly better lows than Omega does - not drastically so, because Pyrrha's lows aren't great either, but Pyrrha's 1K > any of Omega's lows - its range is small, but other than that it's fast, tracks well, and combos into 2B+K,B,B,B on CH. She's also slightly safer - in particular, her 66A is safe against everyone bar one or two characters, whilst Omega's can be punished by more. Pyrrha also has a slightly better throw game, due to oki options from A+G and B+G.
Omega beats her in MANY other aspects though - her damage output is MUCH higher, this is well known. Omega also has excellent block punishment, even better than Pyrrha's (which in itself is good compared to the rest of the cast), with her 236B doing more damage AND having RO potential. And of course there's DNS B... Plus Omega has FAR better guard pressure than Pyrrha does (<3 22_88B and 66B), which helps make up for her poor low game. Both characters have bad BEs, but good CEs, but Omega's is very obviously better here - hella strong whiff/block punisher, raw damage is too good. Her stepkilling ability is more or less the same as Pyrrha's i.e. pretty solid - Pyrrha has a safer 66A, but Omega's comparative unsafeness doesn't make it useless. It's still strong, fast and has solid range. She has other reliable stepkillers such as AA, 22_88K (excellent move BTW, needs more love) and others.
It's pretty hard to argue that Pyrrha is better than Omega - Omega just has a lot of things going for her. One thing that's strange about Omega is that she has a steep learning curve, yet a comparatively less steep playstyle...