Projection Trouble

[Gus]

I am having some projection troubles with some Chinese data. I have
some data that was previously processed and from what I can tell
reprojected to:
Projected Coordinate System: WGS_1984_Albers
Projection: Albers
False_Easting: 0.00000000
False_Northing: 0.00000000
Central_Meridian: 101.00000000
Standard_Parallel_1: 34.00000000
Standard_Parallel_2: 41.00000000
Latitude_Of_Origin: 0.00000000
Linear Unit: Meter
Geographic Coordinate System: GCS_WGS_1984
Datum: D_WGS_1984
Prime Meridian: Greenwich
Angular Unit: Degree

The thing is, I am trying to get it to line up other data that I
believe to be more accurate and in a different Projection:
Projected Coordinate System: Albers
Projection: Albers
False_Easting: 0.00000000
False_Northing: 0.00000000
Central_Meridian: 105.00000000
Standard_Parallel_1: 25.00000000
Standard_Parallel_2: 47.00000000
Latitude_Of_Origin: 0.00000000
Linear Unit: Meter
Geographic Coordinate System: GCS_Krasovsky_1940
Datum: D_Krasovsky_1940
Prime Meridian: Greenwich
Angular Unit: Degree

When putting these two datasets in ArcMap the processed data is
shifted about 500 km East and seems to be about 10 km shorter from
north to south.
I am not sure if it would help but I would like to get the processed
data in the later projection. I've done about 12 hours of reading now
trying to fully understand projections, datums and what not but I
cannot solve this problem.
Any ideas? Thanks.