The success of How I Met Your Mother between 2005 and 2014 cannot be understated, and its consistently high quality drew in a plethora of audiences and built a loyal fanbase. There is no doubt that a lot of this is down to the fantastic characters, the best and most famous of which has appeared to be Barney Stinson, even over main focus Ted Mosby.
There is no doubt that Barney can be a pretty awful person, and does some terrible things, but to say that he is a worse person than Ted is a pretty flawed outlook when examining the evidence.
Worked With The F.B.I
Let's face it, the fact Barney spent years at a money-sucking corporation all for revenge on a guy stealing his girlfriend is not massively heroic, but at the same time, it inadvertently is pretty heroic.
Working with the F.B.I to take down Greg and G.N.B is not something Ted would ever have the gall to do. As much as his intentions may have gotten skewed, Barney did a great thing.
Loved His Family
This is not to say Ted did not love his family; of course, he did. But the way he acts towards Clint and his mother, and then his father, is not like Barney.
Barney lives for his mother and brother and idealized them. Just to avoid hurting her, he pretended he had a full-on family to fulfill her deathbed wish. Admittedly that is a little insane, but love like that can be a little insane.
Knew He Had Issues
Barney knew he had issues, plain and simple. He was aware Bob Barker was not his father, he was ironically open about how he is an innate liar, and, while Barney did hide a lot of his insecurities, he acknowledged them when the time called for it.
Compare this to Ted, a man with severe issues with self-absorption, obsession, attention, serious pretentiousness, and nastiness towards women, with an inability to ever acknowledge these issues, even if he does acknowledge them, he sees himself as a downright nice guy.
Was Better To And For Robin
Ted and Robin got initially shown to be the on/off sitcom love interest of the series, but as time went on, Barney stepped into that role brilliantly.
Overall, Barney was better suited for Robin, healthier relationship-wise, the two grew with each other and made each other better, they enjoyed and appreciated the same things, and actually learned from their previous relationship mistakes with each other. Robin and Ted did pretty much the opposite of all this.
Misunderstood
Being misunderstood does not necessarily make you a good guy, but in Barney's case, it makes him a better guy than Ted.
Barney has a whole host of issues as an explanation for his awfulness, and while that is inexcusable at times, it is understandable once you genuinely get to know Barney. Ted just maltreats people, whines, and is self-absorbed for no real reason.
Ted Treated Barney Like Garbage
It is often highlighted how Barney mistreats people on occasion, but very rarely is that his friends, even more rarely does he mistreat his friends in a non-jokey way.
Ted, though, has to remind Barney that he prefers Marshall constantly. What is the need? You do not see Barney or Marshall ever talk about how they prefer anybody over anybody, and Barney understands that Marshall is Ted's number one best friend. Nevertheless, Ted needs to tell Barney he prefers Marshall every time Barney calls them best friends.
Relatable
Weirdly enough, despite his suave fashion, insane income and possessions, and womanizing ways, Barney is a far more relatable person than what Ted is.
Few people can relate to the combination of Ted's obsessiveness and pretentiousness, only really his loneliness. However, people can relate to Barney having a poor upbringing, no father, an alcoholic mother, a defensive shield, massive insecurity, loneliness, and a genuine struggle to grow when you are genuinely trying.
Far Bigger Problems Than Ted, Never Throws A Pity Party
Continuing with the issue of Barney's deep-rooted issues and troubling upbringing, he may have thought he and his life were awesome, but fans know he was dealing with a lot throughout the show.
What makes him better than Ted with these is the fact he had far more problems deep down than Ted, but never made a big deal out of them, or drew attention to them by way of pity parties. Ted, on the other hand, seemed to make a lot of things about him and his issues of being alone, when in fact it is his insanely high standards and treatment of women that have caused that.
Far Less Selfish
Despite the way the show is presented a lot of the time, when you really think about it, Barney is far less selfish than Ted. Barney does not seek praise or approval for doing nice things for his friends, and on the flip side does not seek pity and attention for when stuff goes wrong, look at when he goes to San Fransisco for Marshall and Lily.
Ted, though, while he has been a good friend numerous times, makes a lot of stuff about him, and his issues, the pilot should have revolved around Lily and Marshall's engagement, but instead, it was Ted's obsession with Robin.
He Grew
The finale definitely undid a lot of the development the characters had undergone throughout the show, particularly Robin and Barney, but even including that, Barney developed an insane amount from the pilot to finale.
Ted was pretty much the same character. While a lot had happened in his life, and his life had changed a bit, he had not. He had the same flaws, same problems, same everything; he was the same guy for nine seasons straight, not growing or developing at all.