An aluminized tarp will block light, so it's dark inside. You'll have to use your flashlight more. This may make an aluminized tarp undesireable.
An aluminized tarp will be very effective at reflecting sunlight, so it would be cooler in warm weather if you're in the sun
An aluminized tarp will radiate less IR, so it won't get so cold, especially under a clear sky, so there will be less condensation. This would be on both the outside and inside. This would be an easy experiment – silnylon and aluminized tarps with people overnight… You could get useful results without people and just small test samples.
A silnylon (or cuben) tarp will block IR loss, especially to a clear sky. You will be a little warmer with tarp compared to no tarp, but the effect is small, maybe 10 degree F. An aluminized tarp would be a little better because it would reflect back the IR, maybe another 5 F. Especially if the tarp was small and you just barely fit into it. You could try to measure in the field but would likely get inconclusive results.
If you're in a meadow, and it's a clear night, regardless of any tarp. it can easily get 20 degree F colder. Better to camp in sheltered area in the trees. Then it doesn't matter if you have a tarp or not. Maybe aluminized tarp would add a little warmth.
Just because an aluminized tarp looks reflective in visible light, doesn't mean it will be reflective in IR. Like, if there's a layer of mylar, with aluminum underneath, the mylar will absorb IR.