I don't think it is as simple as that. Mr Jordan has indicated since book 1 that Logain will play a significant role in the future. Rand foresaw Logain's eventual escape while the man was being paraded through Caemlyn. Many of the characters and their plot threads introduced in the first book are still to be fully resolved. Logain's thread has yet to unwind to it's final conclusion. There is a mere hint that Logain's destiny is greater than merely killing Taim. In TFoh through Min's POV we find out that Logain had wanted to name himself "Guaire" before Siuan shot down the idea and he had to settle for Dalyn. The only other character in WOT named "Guaire" is or was the false dragon Guaire Amalasan who started the War of the SECOND DRAGON. It required a ta'veren of the strength of Artur Hawkwing to stop him from achieving his aim. Guaire Amalasan conquered half the nations and was even alluded to as The Second Dragon. Is Mr Jordan giving us a sign that the exclusivity of the Dragon is an illusion? Could it be that the Creator or even the Wheel is not limited to one Dragon? We know that Rand Al'Thor's one overriding purpose is to face and defeat the Dark One at Tarmon Gaidon. It is very possible that Logain is the Rebirth of Guaire Amalasan whose purpose is to redeem the male half of the True Source, Saidin and thus rescue the entire lot of male channelers from a fate worse than death. It would certainly be a fitting glory for a man who has been gentled, Healed and depicted by Mr Jordan as being the embodiment of MALENESS (see TFoH and the scene in LoC when he stares at Elayne and Nynaeve just before she Heals him. Remember, at that particular moment she was angry at ALL men!!)

As for Taim it is possible that he is nothing more than a former false dragon hankering after his lost glory and jealous of Rand. It is interesting to note that news of Taim's escape came just before that of Rand pulling Callandor and becoming the Dragon Reborn in TSR,chapter 'Deceptions'. Logain's glory is also mentioned here for the first time. In the near future Taim may well try to re-achieve 'Dragonhood' and fail whereas Logain will succeed. I also do not believe that Taim is Demandred simply because at the end of LoC Taim was leading the Ash'aman in battle and in the very last page we see Demandred kneeling at Shayol Ghul. But in the beginning of ACoS we see that Taim is still hangin around the battlefield, shadowing Rand. There is no indication that he had the time or personal space to Travel to Shayol Ghul and back without anyone noticing. Demandred was at Shayol Ghul and Taim was at Dumai's Wells ergo they are two different, separate, personalities/entities whom Mr Jordan has consciously painted alike. There is an overwhelming possibility that their destinies WILL collide, and sooner than we think.