I dont think there is much competition if any. First off it would be both expensive and a headache to introduce the excellent Typhoon into a F-series heavy airforce. They already have a size able F-15k force already with more on the way, so the Typhoon was a no go from the beginning even if the Koreans wanted it to appear differently.
And their F-15k's are already wired into the strike mission with the SLAM-ER, Harpoon-ll, and JDAM. Buying more makes sense from the maintenance ,training, and systems integration front. Adapting a new aircraft from a new maker is a fairly large effort. Far more so then most people think.
Lastly, and most importantly, the Koreans have to balance their aircraft purchases with the threat level they are facing. Perhaps if their Northern cousins were flying the latest Soviet bloc aircraft/weapons, and their pilots were able to log meaningful flight hours, buying the outstanding Eurofighter would make more sense. However the South already has a vast lead in the air to air role and there isn't a great deal of pressure, actually none, to enhance an already large lead in both systems and pilot skill.
The South Koreans have always shown a willingness to buy Yank systems as they rightfully see their alliance with us as the biggest guarantee to their security. Any conflict on the peninsula would also see a significant deployment of the F-22, further decreasing their need for a nimble ATA superiority fighter.
Anyway, that's my take on the situation. As good as the Typhoon is it never had a chance with the Koreans. I'd say it has a far better one with the Japanese as its the best pure ATA choice for a country that cant buy F-22s.