I've seen both and enjoyed Groundhog Day much more than Anastasia (so much so that I returned to see Groundhog Day a second time).
There are many on this board who loved Anastasia, but it looked and sounded like a second-rate Disney knockoff to me. The show ostensibly presents itself as an historical piece, but it came off more as a fairy tale to me.
Groundhog Day runs the gamut of emotions; it's very funny and cleverly staged, but also deals with serious themes. Andy Karl is brilliant in the lead role.
==> this board is a nest of vipers <==
"Michael Riedel...The Perez Hilton of the New York Theatre scene"
- Craig Hepworth, What's On Stage