These two comparable tools exist because ESRI has multiple license levels. Point to Raster (Conversion) is only available with the Advanced license. Feature to Raster (Conversion) is available with all of the license levels.
Point to Raster allows you much more control over how multiple points are handled when multiple points fall within a raster cell. You get the option of most frequent, sum, mean, std, min, max, range and count. Feature to Raster does not allow this flexibility:
This tool always uses the cell center to decide the value of a raster
pixel. If more control over how different types of input feature
geometries are to be converted, please refer to the respective
specific conversion tools: Point to Raster, Polyline to Raster, and
Polygon to Raster.