Any clean filter should not add more than 6 PSI to your total reading with 3 PSI as average so I would expect the difference between the two filters to be much less than 6 PSI. In fact, for similarly rated filters, cartridge filters should have a slightly higher PSI than sand and DE even higher. Also, most of the pressure reading in a filter gauge is due to the plumbing downstream from the filter and not the filter itself.
With a sand filter you also add a backwash valve that can increase the pressure by as much as 6 PSI depending on the valve type. About half of that will be post filter and half pre-filter so I would expect a 3 PSI rise on the guage from that.
So net net, I would not expect much of a rise at all between cartridge and sand. It could just be that the cartridge filter gauge was not working properly. This is pretty common so I would not worry about it too much.
I know the filter is new but have you backwashed it yet? See if it goes down after a good backwash.
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