Does plants grow better with or without worms?

If you don't have earthworms in the soil, there is something wrong with it. Earthworms aerate the soil and enrich it with their "castings". Worm castings are one of the richest types of fertilizers. You can actually buy them in bags. When worms disappear from the soil, it's an indicator that something is amiss. Using chemical fertilizers and poisons to "kill bugs" will also kill earthworms. Keep plenty of organic matter in the soil, such as compost, and both the worms and plants will be very happy.

With worms, they help with the soil

You want a good population of earthworms in your soil. They help move nutrients around, process some into materials the plants can make better use of, etc.

According to my knowledge, there are two kinds of worm which affect the growth of plants namely harmful and beneficial ones; the examples of the former one being aphis, caterpillar, larva, borer, cutworm, army worm, mealy bug, scale insect, locust, leaf-miner, stink bug, etc; while that of the latter ladybird beetle, mantis, parasitic wasp, etc.
Yip

basically worms are useful - their excrement is a good fertilizer

That does depend on the type of plant.

Most plants grow better because worms open up the soil and make it less hard.

Some plants do better without worms. Some trees depend on coverage by the leaves from last year to keep competing trees down. The population of trees in the northeastern US is slowly changing for this reason among others. Some trees leach acid that is neutralized by worms. Pine needles are acidic. Some plants like hard soil. Worms are not good for most cactus species. There are bound to be a few more exceptions but vastly more plant species do better with worms.

with

With worms in the soil, they help with the soil.

You mean "do" plants grow better. Yes, they grow better with worms in the soil.

Earthworms and plant growth - view this science fair projects. ... The presence of earthworms in soil will help plants grow faster. ... containing earthworms grew taller than the plants that grew in soil without earthworm