^He does have less budget than RTD, I believe he said so before series 5 started but he hoped he could make it so no one would notice. I believe BBC America made up some of the difference this series though.
In Season 5, I can't tell the difference. Season 6 it feels a little more obvious. So many of the episodes are such claustraphobic scare-fests. That's great when it's one or two a season but an entire season of them is getting a bit old. But then, maybe those episodes are making up for the major expenses of location shooting in Utah for "The Impossible Astronaut," "Day of the Moon," & "The Wedding of River Song." Those episodes look like latter-season X-Files, when that show had more money than they knew what to do with.
As for making Doctor Who more accessible, I suppose it depends upon what kind of people you want to make it more accessible to. I think of my mother. She is not a sci-fi fan at all. She's never understood my love of Star Trek and will openly mock me when I'm watching Stargate SG-1. However, with judicious episode selection, I've made Doctor Who a surprise crossover hit with her. The trick is to only show her the episodes with a solid emotional through-line (or episodes that are intuitive enough to be fun). She has no patience for Daleks or any other episode that relies too thoroughly on sci-fi action/adventure conventions.
So what proportion of episodes have proven acceptable to her?
From the RTD era: "Rose," "The End of the World," "The Unquiet Dead," "Dalek," "Father's Day," "Tooth & Claw," "School Reunion," "The Girl in the Fireplace," "The Shakespeare Code," "Blink," "Partners in Crime," "The Fires of Pompeii," "The Unicorn & the Wasp," "Silence in the Library," "Forest of the Dead," and "Midnight."
(Plus episodes I've been meaning to show her but haven't gotten around to yet: "The Empty Child," "The Doctor Dances," "Bad Wolf," "The Parting of the Ways," "Smith & Jones," "Human Nature," "The Family of Blood," and "The Next Doctor.")
From the Moffatt era (Season 5 only): "The Eleventh Hour," "The Time of Angels," "Flesh & Stone," "The Vampires of Venice," "Amy's Choice," "Vincent & the Doctor," "The Lodger," "The Pandorica Opens," and "The Big Bang."
So we're looking at 24/59 (40.68%) for RTD vs. 9/13 (69.23%) for Moffatt. And that's not counting the episodes that I thought she might like that really backfired, like "Dalek."
In terms of doing stories that you don't already have to be a sci-fi fan to get, Moffatt gets the clear edge in my book.