It might be interesting to read the following two documents that compare interpolation methods:
To bad that you don't have access to the source data, since a TIN would not be the best option to create a surface from contour lines. There is a tool that does this better: Topo to Raster—Help | ArcGIS Desktop
Another thing that might be interesting is to know that each triangle in the TIN already holds information on slope and aspect. You can also use the TIN Triangle—Help | ArcGIS Desktop to generate a featureclass that have the slope for each triangle.
In case you cannot decide, do them both (linear and natural neighbors) and compare the differences (Minus—Help | ArcGIS Desktop ) and see where the largest differences are and which one to your opinion is closer to the truth.