If BB were asked and answered honestly I think he'd tell you it was a mistake to choose Vereen over Woodhead. Lewis gives him a better version of Danny.
And like you said, White is a Vereen replacement, not upgrade. White still hasn't shown he can run the ball, something Vereen also never did in 4 seasons.
I don't really agree with the above. Loved Woody, he had a fantastic first season with us, but by the end, his rushing yardage and average had declined each year, and he was turning 28 when BB decided to move on.
Woody went to San Diego, rushed for 4.0 yards per carry like his last season in NE, then got injured the next year after 3 games. So far this season, he's averaging 3.7 YPC, albeit with an extremely small sample size, but he's rushing for 3.8 YPC over his Chargers career.
If there was one regret, it might have been not having Woody for depth when Vereen got injured and missed half the season. But Vereen had a much better 2013 than Woody. Let's review (and remember Vereen played half the games that Woody did):
2013 comparison (rushing stats first, YPC is yards per carry/passing stats, YPR is yards per reception/ average yards per game)
Woody: 429 yards, 4.0 YPC/605 yards, 8.0 YPR/64.6 YPG
Vereen: 208 yards, 4.7 YPC/427 yards, 9.1 YPR/79.4 YPG
Woody wins on volume, but Vereen was more effective when he played. And Vereen missed the early to mid part of the season, so he was still available in the play-offs, where he played just as well as Woody.
Play-offs
Woody: 3.5 YPC/4.8 YPR/54 YPG
Vereen: 5.7 YPC/10.7 YPR/61 YPG
In 2014, Woody got hurt and missed the last 13 games of the season. Vereen was healthy and while his averages dropped a bit from the previous season, they were still comparable to Woody's last season in NE:
Woody in NE in 2012: 301 yards, 4.0 YPC/446 yards, 11.2 YPR/46.7 YPG
Vereen in NE in 2014: 391 yards, 4.1 YPC/447 yards, 8.6 YPR/52.3 YPG
It's also worth noting that Woody hasn't lit it up since leaving either. Part of this is playing for the Chargers, no doubt, but part of it might also be age or deteriorating skills.
Woody in NE: 4.8 YPC/10.7 YPR
Woody in SD: 3.8 YPC/8.1 YPR
And I think we remember that first season so fondly, we overlook the next two.
Woody in NE in 2010: 5.6 YPC/11.1 YPR/66.2 YPG
Woody in NE in 2011/2012: 4.3 YPC/10.4 YPR/40.5 YPG
So I don't think Woody was really a huge regret for BB. He's been solid, although slipped a bit since his peak, and Vereen certainly filled that void more than capably. And Vereen has performed much better in the play-offs. These are small sample sizes, but FWIW:
Woody in NE in play-offs: 3.4 YPC/9.4 YPR/38.5 YPG over 6 games
Vereen in NE in play-offs: 5.0 YPC/10.1 YPR/64.7 YPG over 7 games
As for Vereen's running capabilities, he wasn't a consistent guy, but he wasn't all that bad. He averaged 4.2 YPC for his Patriots career, just like Kevin Faulk, and I don't think anyone is saying Faulk could never run the ball. Woody's Patriots career average is higher because of that sparkling 5.6 YPC his first season, but he averaged 4.3 his next two. So I don't know how we can be critical of Vereen as a runner while applauding Woody, who has consistently declined since that first season.
Not trying to trash Woody, but I don't think BB regrets that decision.