I have never used shielding paint, so I won't address it here, but I have used copper tape sold by places that cater to guitar building and repair. I have also used Aluminum HVAC tape, and have commented many times on the forum that it works quite well, at a fraction of the cost of other alternatives.
I just finished a guitar for my daughter, an offset body with strat electronics. In the process I discovered is that not all HVAC tape is created equal. The adhesive on some is not conductive. I have a couple of rolls at home and one is conductive, the other is not. Meanwhile the adhesive in the copper tape I had left over plenty conductive, but there was not enough of it to do the whole cavity. Since I had already shielded the guitar with the not particularly conductive tape, I cut some thin strips of copper tape to connect the highly conductive aluminum surfaces. It worked like a charm.
So...is copper tape better? At least with the copper tape I had on hand, yes, because of the conductive adhesive. But thin strips of it will make even bad HVAC tape just as effective. Good HVAC tape is still a pretty good alternative I think, but I am taking my multi-meter to the big box store the next time I buy it ;-)
While it is also true that it is very difficult to solder to alu tape, I have not actually found it any easier to solder to copper tape. Some folks manage it so YMMV. With both types of tape, I wire a ground wire to a piece of tinned metal that I screw down.