Pros:
A) They shoot perfectly right "out of the box". I mean consistent .950" at 300 M with .338 Lapua 250GR Scenars (and I'm a "barely adequate" shot). The .308s are no different. Further out the rifle will shoot as well as you can read the wind for the cartridge you're using;
B) They are virtually indestructible and built like a proverbial tank. They are an army guy rifle which means they were designed for something more than sitting on a shooting bench while being slouched over by Mr. Big Boiler. I've humped one all over hells half acre and subjected it to all kinds of real world brutality to no effect;
C) Require no fiddling *ucking around whatsoever to make them work; and
D) With the adjustable cheek piece and butt the ergonomics are very good IMHO.
Cons:
A) Price - big, big dollars

. Though, in their defence, buy one once and all you will ever have to replace are barrels (which you can easily do yourself without a gunsmith). There is nothing you can really upgrade to in terms of a production rifle. While DSRs are wickedly nice you aren't getting any more on target performance from them and smashing around the bush with one is analogous to taking your Ferrari Enzo 4X4ing. Before the custom boys immolate me I should note that a number of gunsmiths here and in the U.S. can build excellent rifles for less dough (in fact my next .308 will be a custom).
B) Limited bullet selection in the .338 platform. My .338s' magazines can't handle 300GR bullets because of the overall cartridge length. For some this is a fatal limitation. Again they are army guy guns designed to shoot factory match ammo.
C) Aesthetics - could be argued as both pro or con. They are to precision rilfes as Glocks are to pistols (utilitarian tools of consistent and predictable performance with no attention paid to how they look).
D) They demand good glass which is even more shekels.
You might want to check out:
http://demigodllc.com/articles/military-338-lapua-rifles-trg42-awsm/