Phantom would definitely be a better choice for ant control because it is a non-repellent which also has a transfer effect so it will be transferred back to the colony to wipe out the whole colony vs just the ants that cross over the treated area. The downside to this is that there is a delayed reaction kill which means while it will kill spiders, it will take a while for them to die. Phantom is only labeled for spot and crevice treatments around potential pest entry points such as pipes, wires, vents, window frames, etc and is not for perimeter spray treatments.
Phantom is not labeled to treat carpet beetles. For indoor carpet beetle control you may want to consider a product such as Nyguard Plus. This product contains an insecticide to kill the roaming adults and an insect growth regulator to stop the harder to kill immature beetles from reaching a reproductive state which in turn will break the cycle of infestation. As an added bonus this product also contains a deodorizer for carpet applications. You should apply every 2 weeks.
It does take quite some time to fully eradicate carpet beetles, how long depends on how bad of an infestation you have and making sure you have found the source. Please take a few minutes to read our Carpet Beetle article to learn more about eliminating a carpet beetle infestation.