I prefer the original Organization, though they have a advantage of being in more then one game. That being said they were not a perfect villain group. As stated by
@palizinhas there were a lot of filler Organization members in the old group. Members like Lexaeus, Larxene, Zexion, and Luxord served no unique role in the group that made them invaluable. They really didn't earn that name Organization 'XIII' when in all their major games they are split. They were mainly Organization VIII for the longest of times, and most of the time they are only relying on their Keybladers to do any of the work for Kingdom Hearts.
In the new Organization pretty much every character was important or will be important in future titles, and had a job to do for the Seekers, so none of them were filler. But they were also not a real group. They were just 13 characters isolated in their own stories and only the ones who know each other from the old Organization were allowed to interact. The 13 Seekers of Darkness never even held one group meeting with everyone present to interact and play off each other.
The original Organization mostly had their own thing going on but they did interact even if it was small or just passing comments. Xigbar, Demyx, Xaldin, and Luxord had no story involvement in the RAX stuff, but they still commented on it throughout Days especially towards the end. And in KH2FM we see more of the meetings and characters interacting and chatting about the Sora/Roxas/Axel situation from time to time. They did at least feel like a group. Plus there was more backstabbing and behind the scenes politics going on with the original, helped of course that they had more then just one game to be in.
And between the two Organizations, the first ones goal was to obtain Kingdom Hearts to get their hearts, and mostly everyone was on board with it. The 13 Seekers of Darkness all wanted like different stuff, and are not united. I don't even think Xehanort knows all his vessels names.
Long story short, both groups have their positives and negatives. But the original had more going for it for me to say they were the one I prefer.