When I added a radiant barrier to my attic, the attic temp dropped over 30-degrees on a hot summer day. Prior to this, the insulation got heat-soaked (about R35) and the ceiling was hot by the end of the day. After, the ceiling was the same temperature as an interior wall. Really impressive for a sheet of paper with some foil facing. It's just stapled to the underside of the roof rafters.
Fiberglass insulation, I presume?
Fiberglass is somewhat translucent to infra-red radation, taking several inches if depth to absorb it to 90% level. The result under a high radiant heat flux is that the insulation heats up in internal layers, and typically hottest place in the insulation is 1-2" below the upper surface, making it 10s of degrees hotter than the attic air on a hot summer day, so instead of R35 insulating against say a 130F attic, you have ~R30 insulating against 140-150F insulation. The upper layer of the insulation itself transfers that heat to the attic air via convection loops in the upper inch or so of insulation.
Cellulose is opaque to infra-red, and while it's upper surface heats under high radiant flux, the surface temp is closer to the attic air temp, and you have benefit the full R between the attic air and conditioned space.
But with a radiant barrier both types of insulaion run cooler when the radiant heat transfer between 150F roof and attic floor interrupted with reflective insulation, but the effect is more pronounced with fiberglass than with cellulose. (There's tons of research on this available on the web from Texas A & M archives, as well as the Florida Solar Energy Center, and multiple other sources.)
If the joist tops are exposed, wood is very absorptive of the radiated heat, and has far less R-value. This too can be mitigated with reflective insulation, but even 3" of cellulose over the joist tops as a thermal break can be more effective in reducing the total heat flux into conditioned space, and has much bigger heating-season benefits than radiant barrier, which often increases the heating load during the shoulder seasons in heating dominated climates, since it runs the attic cooler on sunny spring/fall days too, not just winter. The roof deck is an unglazed solar collector with signficant benefit during the shoulder seasons.
In all but the hottest, sunniest cooling dominated or mixed climates radiant barrier isn't typically cost effective if you already have more than R30 of cellulose that includes thermal breaks on the joist tops. It'll cut your peak cooling load, but not enough to make it pay. But if you have only R19 (as is common in coastal CA) it's cost effective, but not as cost effective annually for many/most as bringing the total R to R30-40.