Do I have to choose? Both are excellent brands. SEIKO mechanically might even be a superior watch... I am referring to the high end line, Grand SEIKO, etc. Seiko initially marketed to the USA relatively inexpensive watches, thus when many in the US think of Seiko they think inexpensive quartz watches... not true.
Seiko movements dominated the Swiss watch industry's Neuchtel Chronometer competition in the late 1960s as did Omega. “ Google Seiko Swiss Watch Competition.”
Seiko has always been an innovator in regards to their movements. Many are unaware that Seiko produced a limited edition of 8 pieces, the Credor Fugaku Tourbillin, which sold for 500,000 Euro.
Now, if you asked me, do I wear my Omega Speedmaster 105.012-66 more then my Seikos...... you bet. But, they are both superb watches.