It is very hard to get a good result when gridding contour data. Contour data tends to be closely sampled along the contour line but those lines are widely spaced. Furthermore, the distance between lines varies significantly (depending on slope) and the direction from one line to the adjacent lines varies continuously.
In MapInfo Pro Advanced you have a choice of four methods - Minimum Curvature, Inverse Distance Weighted, Triangulation and Natural Neighbour.
IDW will almost certainly fail - and do so grotesquely. To help the algorithm you ought to use search sectors and only the nearest stations, but the orientation of the search sectors needs to be perpendicular to the lines - which you generally can't achieve with contours. It is very hard to get an acceptable result.
Triangulation will do OK, but the result is not smooth. You need to apply some post-processing smoothing and that is always lamentable. Also, instead of triangles joining adjacent contour lines (which is what you want) you tend to see the triangles generated along the lines as they fill in the gaps in the detail in the contour line. This results in flat areas running along each contour line.
Natural neighbour has a triangulation engine behind it, so it tends to suffer from the same problems. However, it does do a reasonable job between contour lines. It is not a total bust.
Minimum curvature is probably the best choice, but it also struggles. You should not be tempted to use a small grid cell size! This is important with minimum curvature. If your original DEM raster had a 20m cell size, then the contours tend to have a node every 10m and you might be tempted to choose a very small cell size like 2m to 'preserve the detail'. Instead you need to look at the average distance between the contour lines and choose a cell size that is a reasonable fraction of that (1/4). Even so, you will tend to see plateaus running along the original contour lines. You can reduce the tension in the splines (to zero) and increase the number of iterations to reduce these, but only marginally.
One possibility - for the future - is to use a locally adapted minimum curvature algorithm. The minimum curvature operator can be biased in a particular direction and this can be varied locally. For gridding contours, you could continually vary the bias by choosing the direction of maximum slope - i.e. the direction of the closest contour line. For other applications choosing the direction of most dominant trend is best.