In this world of entertainment broadly there are two different groups. One which is an anime fan and one which is not. Most of the people think that anime is for children whereas the truth is anime is one of the form of animation. Some of the Western and Asian audience don't know this basic difference. Anime likewise TV/Webseries have different genres like sci-fi, suspense, romcom, sitcom etc.
The difference is presentation. Everything in a series is presented in real and tangible world with real humans playing a character and visiting real locations, eating real food, performing real actions. Exactly vice-versa is the situation in an Anime. Nothing is real, not the characters, not the locations and not the action, Everything is an art. The only real thing in this whole anime project is voice. Talking about music the medium in both the projects is same. Though Anime Music is quite an intense one.
The one thing which is more advantageous in Anime production is the quality imagination and fantasy in low budget. Yes a low budget if we compare it with TV/Webseries. (Note- Rest of the factors are not considered). Hence Imagination in terms of Visuals, story and characters and most importantly emotions is sometimes way beyond than what we can ever see in a TV/webseries.
But one common thing we can see in many Animes is a fantasy or mythical world. Some kind of intangible Power a character have or is present in the story. That's the strong point of these Manga writers or Anime Scriptwriters. A possible reason behind this is that Japanese people love to watch such scenarios, situations, to hear such stories which are not real at all. For eg. there is a book/diary in which you will write a name of a person (Maybe whom you hate a lot) and he is dead. Majority of the population may want to have such diary or a book and that's what clicked the mind of writer when he first thought of the most popular anime DeathNote. Same goes with many other Animes. Second thing Animes focus on is emotions. We can see a variety of emotions in one Anime which we might two three different TV series combined.
On the other hand TV Series are the inception of majority of the ideas that are there already but not presented. The ideas and the concepts which they present are the real power. For eg, a TV Series like Friends or Big Bang theory is something nobody would have previously thought. Yes when four five friends come together, fun is bound to happen and memorable moments are bound to get created. Yes Western world is also not behind when it comes to mythology or fantasy. Harry Potter (though not TV Series), Witcher, Game of thrones are some of the best examples where we can see the real efforts are taken to set up a mythical world. Hence this format focuses more on perfection/logic in presentation of idea which sometimes is missing in the Anime.
In 1990s when western world have superheroes like Superman, Batman, Thor, Captain America, which were already popular though comics from around 1940s, Japan on other hand in 1990s came up with one of the legendary Manga and Anime in current age, Dragon Ball Z. A whole new concept may be somewhat similar to Superman story but with a lot of variation where a boy from outer planet arrives on planet earth. The boy is from the Saiyan clan (Originally adopted from a classic legend of Monkey Kind) leaving on some different planet. Now lets break the story of two classic and legendary super heroes and understand the real difference between the thinking of two Legendary Writers-
Superman- A boy named Kal-El from planet krypton, Sent to earth because the clan wanted to save their last descendant from the evil powers. Hence he arrives on the earth and found to a middle class family who raise him well. Through his journey to become Superman many times he have felt the difference between him and the normal humans and one he discovers the truth and become the legendary Superman.
Dragon Ball Z- A boy named Kakarot from the extra terrestrial clan Sayians ruling the universe was sent on the earth for a mission to conquer the earth. But here he meets a Martial Artist and was taken care of. While he was taken care of he suffers head injury and forgets his mission to conquer the earth and then the new personality in him trains hard, take up challenges and encounter some aliens as well to become on of the most popular and legendary Anime Super Hero known as Goku.
Believe me these both the above series have been an inspiration for thousands of writers around the world. Both had raise and set up new standards. Both had raise expectations from the entertainment world at the respective times.
Hence its quite difficult to choose one of the format which could be the best. Both the formats are better in their own way. But what see is the inception of a concept is what TV series do and to make the concept more and more interesting, fascinating and engaging is what the Anime does.
Image source- Google