Two thrillers with literary antecedents — "Cross" on Prime Video and "The Day of the Jackal" on Peacock — premiered Thursday. Each series is a cat-and-mouse story, with the hero and the villain identified from the beginning, though exactly who is the cat and who the mouse is an evolving, revolving situation.

Based on a character created by James Patterson (and featured in 32 volumes so far, three of which have been made into movies), "Cross" is a serial killer tale set in Washington, D.C., with detective (also Dr.) Alex Cross, the dedicated lawman. "Jackal," from the 1971 Frederick Forsyth novel (his first), twice adapted for the big screen, is set all across Europe and into western Asia and has little to do with the source material other than featuring a master assassin as its code-named eponymous villain.

Their plots are essentially straightforward — somebody wants to kill somebody, somebody else wants to stop them — but stuffed with complications and characters that can at times muddy specific goals and motivations. You may want to take notes.

That "Cross" is a serial killer series is not out of line with the Patterson oeuvre. The killer in question is Ed Ramsay (Ryan Eggold), and we will spend an exhausting amount of time watching him at work.) He is very blond and buffed — not buff but, like sanded and polished. He regards himself as an artist, has lots of money, is well-connected in power circles and is withal the very model of a modern fictional psycho killer.

When a former gang member turned activist is found dead, Cross (Aldis Hodge) is trotted out with partner John Sampson (Isiah Mustafa) as "dark skin cover" for the police department but also for their contacts within the Black community, though, as police, many in the community regard them with suspicion. ("Chief," Cross asks, "are you trying to solve a crime or a PR problem?") The authorities are lazily blaming the death on suicide or an accidental overdose, but Cross, who knew the victim, smells murder. And when a second killing occurs, he's convinced there's a link.

Like many screen detectives before and after him (the first Cross book was written in 1993), Cross has a dead wife from whose murder he has not recovered, as much as he insists he doesn't need help and as much as everyone around him insists that he does. Does her murder have anything to do with these other killings? That would be telling. But you might guess.

Created by Ben Watkins, the series is solidly made and stylistically straightforward but does suffer a bit from its split personality. Baroque murders aside, and a modicum of genre cliches — an aggressive reporter, for instance, getting in our heroes' way — it's rooted in humans being human, and as absurd as everything is to do with Ramsay, the detectives, their families and friends live in a nicely sketched community in a well-drawn, relatively real world. (Even though it's Canada pretending to be D.C.) Cross comes equipped with two young children and a romantic possibility in the form of Samantha Walkes' Elle Monteiro. But above all, Hodge and Mustafa are charismatic performers with an easy rapport that begs for a reteaming.

Where "Cross" might be said to have a matte finish, "The Day of the Jackal," created by the Northern Irish novelist and screenwriter Ronan Bennett, is high-gloss. Set in a variety of sexy locations, some of them actually where they claim to be — including England, Turkey, Croatia, Estonia, Spain and Germany — it, too, is a serial killer story in a way, though the resident psychopath, the Jackal, kills people for money rather than to gratify some bizarre psychosis. (He does have some backstory trauma, which I suppose is intended to help us feel for him, but, eh, not so much.) Here again, our many-aliased killer (Eddie Redmayne) is something of a mastermind with complicated plots to hatch and a life of luxury led off-hours, not that he gets many of those.

A master of disguise, the Jackal first appears in elaborate — yet, to the viewer, obvious — prosthetics to make him look like a specific janitor in a building he's planning to breach. That this caper results in a staggering amount of collateral damage — I mean, he shoots a lot of innocent people — makes him immediately unlikable, which I don't think is the point; if anything, there's some attempt to humanize him, give him some depth. (Redmayne does do a good job of playing a person who feels that he's nicer than he actually is.)

And for all that we're meant to regard him as supremely gifted — in a sort of teaser assassination early on, he nails a nearly impossible shot, which sets MI5 agent Bianca (Lashana Lynch), who knows about guns, thinking — his answer to just about any difficult situation is to shoot somebody. (Or everybody.) Indeed, this becomes so routine it can hardly be called suspenseful, apart from wondering if maybe the writers will send him in a different direction the next time.

Forsyth's novel, closely echoed in Fred Zinnemann's 1973 film, was based in relatively current events, an assassination attempt on French president Charles de Gaulle by a veterans group disgruntled by Algerian independence. Here, the sights are turned on a progressive tech genius (Khalid Abdalla) who is about to release an app, called River ("River is transparency, River is global change"), that will illuminate the flow of the world's dark money. This has, naturally, has made him unpopular among the world's billionaires.

Though Bianca's doggedness mirrors the Jackal's — they also share certain work-life problems — Lynch's innate soulfulness softens her character. You may question Bianca's choices, but the actor is good to watch whenever she's onscreen. Also shining a light is Úrsula Corberó as Nuria, the series' nicest, sanest, least compromised person, whose entire character has for no good reason been declared a spoiler, even though she's essential to clarifying and/or confusing the issue of how bad or good the Jackal really is.

It's an obviously expensive production — when you follow a highly lauded big-screen classic, even by 50 years, you can't go cheap — with the touristic exotica that's characterized every Bond film since "Dr. No" and money spent licensing Radiohead tracks. There's a good deal of violent action, not all of it involving guns. (A second adaptation, "The Jackal," from 1997, was critically drubbed, though it didn't prevent the film from grossing more than twice its budget.) There are car chases, and a car and horse chase.

Obviously it's a creative choice, in both series, to spend quality time with the killer. And to be sure, a significant portion of the viewing public scarfs these characters and their nasty business like candy corn. The stop-them-before-they-kill-again narrative means that the plot is always activated. But really, there is nothing as tedious as a psycho killer, except when it's a song by the Talking Heads. No matter how you dress them, whatever complicated motivations and methodologies you cook up, they're all cut from the same pattern. Mine is probably a minority opinion, I know, but it's still a free country.

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'CROSS'

Rating: TV-MA

How to watch: Prime Video

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'THE DAY OF THE JACKAL'

Rating: TV-MA

How to watch: Peacock

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