That depends on the values you are attempting to calculate, and the relationship between the two layers boundaries (how coincident they are). Since it sounds like they're numeric values, a spatial join is probably not the way to go. Also note that the right-click join method doesn't give you full control over a spatial join as the GP tool does.
I'm not entirely clear on what you're trying to do from your description, but there are two concepts you need to know about - aggregation and apportioning. Aggregating means combining to larger, while apportioning means dividing between. We have tags for those, so if you search you'll get more info. In some cases you must first apportion before aggregating.
Say for example you have polygons A, B, C, D that all partially fall in polygons 1 and 2. You want to know the total of ABCD for each 1 and 2. First you would have to apportion ABCD to 1 and 2, then aggregate those results to get a total. If you're looking at a geometry property like area, a straight up overlay will do this. If you have a numeric attribute value, the apportioning is usually done by area (meaning percent area A1 of total area A times attribute value is assigned to A1).
A spatial join doesn't do this. It is considered an overlay operation, but it doesn't divide up the inputs at all. You either get one match (first record found) or multiple matches. There are any number of reasons why the join method would produce different totals than the inputs. There are three other overlay operations that could do what you want:
- Intersect only returns areas of overlap (A and B)
- Union returns all areas from both layers (A or B)
- Identity will return all areas from one layer but cut up according to
the other, but requires an Advanced license. (A, A and B, but not B)
The main choice is whether you care about the areas that don't overlap. And in ArcGIS, if you do need to apportion values, you will need to create feature layers, specify a ratio policy when creating said layers, and then run your overlay tool on those feature layers (see Apportion Neighborhood Information to Census Tracts for details).