I actually had some hope, and still do... as it stands, weekly White Dwarf/release isn't a bad thing, it could get people into stores (even if it's just the digital one). However, the execution's not quite there yet. This week's is a decent enough start though.
It's got the expected release list, which I actually like a lot more in weekly chunks. There's a few decent columns, some discussion and new rules for a model. All in all, 4 of these probably add up to a bit more reading than an old monthly WD. Can be turned into something quite nice with a modicum of effort I think. Add to each issue some of the old popular content (batreps, I'm looking at you), maybe sell an (ebook) bundled version every month.
Visions though... To be honest, it strikes me as something that missed it's sell-by date by 10-15 years. It would've been great to have back in the days of slow and barely-there internet. There's still a lot of pretty pictures, but... yeah. It's got some of what the weekly needs to be good, but substantial content is too thin on the ground and I've no idea how they can turn that one around.
Ask not the Eldar a question, for they will give you three answers; all of which are true and horrifying to know.