It seems that this is due to the fact that DirectX uses a left-handed coordinate system and XNA a right-handed one.
Actually, as far as I know, no part of DirectX is intrinsically left- or right-handed, you can use the system you prefer. The math functions in XNA are right-handed, but SharpDX provides both left- and right-handed versions. If you always use MathUtil.FooRH you shouldn't have to change anything more dramatic.
However, I'm not sure what rasterizer state XNA defaults to. Make sure to set the appropriate cull mode (clockwise or counter-clockwise). That should take care of models being displayed "inside out".