Not being a human, he doesn't share the pain of others anymore when accessing them, he can help them without suffering at the same time. The problem is this means he lost his ability to empathize, he can identify the problem and correct it, but all in a very detached way, he is not connecting with others anymore. He becomes complete, happy, but similar to a robot that is controled by one single directive - although with a sense of fulfillment.
I don't understand where this impression of Cole (or any self-aware spirit in general) being or a robot, or incapable of "real" emotion, or unable to form "real" bonds comes from. The fact that he is so happy and fulfilled and at peace contradicts that right out of the gate -- he is Compassion, not Joy or Peace or whatever. If he was merely a robot, he would feel no fulfillment when he helps others, nor the despair that is his greatest fear and evil mirror when he can't help. He's also shown to feel relief, gratitude, fondness for certain indiviuals, grief, distress and conflict as well as the ability to psych himself up for dealing with such situations. And that's just from dialogue exclusive to the more-spirit path -- many of Cole's lines remain the same no matter the outcome of his quest. Plus, curiosity if a known trait of spirits, even those who (like Solas' friend Wisdom) do not actually want to cross over into the mortal world. The same is true for the ability to feal fear and pain, and acting on such feelings out of self-preservation. They have also been portrayed as feeling love and care for individuals and whole communities. Even if we ignore Solas' friendsips with spirits because he is a rather special case, there's also Wynne's near-lifelong bond with Faith, or the mutual love between the Augur's apprentice in JoH and the spirit who has joined with her as a combination of teacher and closest friend.
Compassion is Cole's dominant emotion, of course, because it is his nature. It colours and drives most everything he says and does to an extent we probably can only begin to imagine, and he lacks the first-hand grasp of certain more complex mortal issues, but that does not mean that either his empathy or his other emotions are somehow unreal.
Spirits can learn while still remaining themselves. In one of his banters with Cole, Solas mentions that it's contact with this side of the Veil that develops that ability. Contact, not aping mortals or being here physically.
Really hard decision, but I think I will go with the spirit path because I believe judging what is better for him from a human's POV is inherently wrong. We should try to look at it from the perspective of a spirit and I think Solas is the best one to listen on this.
This I fully agree with, although Trespasser utterly tanked my opinion of Solas. The fact that spirits (at least the self-aware ones) are individuals and people and worthy of being recognized and respected as such is one lesson I'm grateful he helped me learn, though interacting with Cole did most of the teaching.