Is British TV Crime Drama Better than U.S. TV Crime Drama?

Probably.
Throw me any good U.S. show and I'll put up a better U.K. offering (or original). The  U.K. shows I am prattling on about are all free-to-air television (as opposed to HBO and other U.S. cable networks).
Those C.S.I. <insert interesting U.S. city here> series are running out of puff.
You get more bang for your buck with British crime shows, particularly featuring psychos. Take a recent episode of BBC's "Silent Witness" (it started a decade before C.S.I Crapola started). You had a serial killer that made Joe Carroll from "The Following" look like Mr Rogers. All in two (1 hour each) episodes.
Take ITV's "Broadchurch" for superb character development. "Wire in the Blood" for tormented, gifted profilers, long before Will Graham in "Hannibal". "Waking the Dead" also blitzes its U.S. counterparts.
Then you have three more ingredients to add more texture - the British class system, historical locations and eccentric (nutbags?) characters. Take "Midsommer Murders" (please, some wags would say).
Take the Brit's heritage of murder whodunits - Agatha Christie, Sir Arthur Conan Doyle, G.K.Chesterton, Ruth Rendell). The Brits do 'gritty' as well as graphic. Take old episodes of "The Bill" - even minor characters were so well cast, the acting so polished. I remember the high quality of 1960's shows like "Z Cars" and "Softly, Softly".

Don't get me wrong, there are a few standout U.S. stars of the genre: I'm sure you can think of others...like "The Sopranos" and "The Wire" (both cable, though).
"Hannibal" is remarkably brave and multi-layered for free-to-air television. "Dexter" (HBO) was groundbreaking, hope the last season goes out with a bang.
Then to add confusion, we have U.K./U.S. co-productions like the delightful "Ripper Street".

"Broadchurch" ITV Series 1 final episode Episode 8 review Season 2

When I started watching this crime series I thought it was too drawn out, a bit like "Top of the Lake" goes to Dorset. What is it with bleak, desolate places and dark secrets. Ask anyone from Adelaide. Oh dear, I have offended my wife. I will retract that remark or I'm cooking for myself tonight.
By about Episode 5, I was sucked in. Probably when Pauline Quirke came into it. The characters are well fleshed out, the interweaving of stories compelling. Lots of grey, tortured characters. This show would had  less rounded characters and more car chases if it had been on U.S. free to air.
David Tennant shows what a fine actor he is. Olivia Colman (a delight as the mum in "Beautiful People") played well opposite him as DS Ellie Miller. Her scene when told the truth about her husband was heartbreaking. Ellie's whole world is upended.
In fact the last 20 minutes of the show was almost too painful to watch, albeit beautifully acted. The uplifting beacons along the coast was a moving final scene.
One wonders who will be featured in the series 2, as the two leads seem to have been written out (DI Hardy's heart condition, DS Miller can hardly stay in town).

UPDATE
Season 2 Knocked my socks off.
Tennant and Colman return. Only the Brits could get away with this so flawlessly. It's now not: who-done-it but a did-he-do-it? Charlotte Rampling (so wasted in the atrocious final season of "Dexter") chews up the scenery.
Rarely do you see a second season surpass the first.