My garden has lots of trees in it, making a very rooty soil that is hard to grow anything in, so I plant (mostly herbs) in pots and place these outside in the garden.
I was wondering if theoretically, assuming a pot size that is suitable for the given plant, if they can grow as large and plentiful as those planted directly in the soil?
In theory, yes, but it's dependent on which herb and its ultimate size, pot size and environmental aspects (soil type, watering, fertilisation). Certainly smaller herbs such as common thyme will do well in the right size pot, but creeping thymes and other creeping herbs won't necessarily spread as far as they would in the ground unless they are planted in something much wider than an ordinary pot. Rosemary, ultimately a large shrub, will usually not achieve its full growth potential - in the ground in the right conditions, it will make 6 or 7 feet tall and wide when mature, but its growth will be constricted in a pot, unless it is regularly moved into larger containers with the final one being impractically large. The same applies to Bay laurel, which are really trees anyway, but for both plants, you will get some years of useful cropping before the plants become stunted.
There are obvious advantages to growing in containers - the right kind of soil conditions are easily provided, and the containers can be moved around when necessary, perhaps for protection in severe weather, or to catch more (or less) sunlight. The disadvantages are that plants in containers are more or less entirely dependent on you to provide sufficient and timely water, to provide fertiliser if required, and to pot on into larger containers when necessary.
If the pot size is suitable for the given plant, there is no reason for a potted plant to not grow identical to ones planted directly in the soil.
However, the qualifier here is the word suitable. Roots of many plants go meters to tens of meters deep when mature. If such a plant is potted in even a relatively large pot of a meter depth, it is not likely to attain its full potential. This is because its root will run out of space to grow, and thus limiting the growth of its overground parts. On the other hand, herbs, many of which are perennial or biennial, have shorter roots and will flourish identically in pots.
Ultimately, it depends on what the gardener wishes to achieve with the plant. The gardener may be interested in flowers or fruits, and in such cases it may be even desirable to have a plant of smaller size, as many flowers or fruits of a large tree would be out of easy reach. Big plant species are potted in small pots as part of the process to create Bonsai, where the goal itself is to make a small plant. Home gardens are almost always constricted of space, and in that case, potting plants is the more sensible choice. As mentioned before, potted plants are easier to manage, and their flowers and fruits are within reach of the gardener's hands.
In your particular case, as you are interested in mostly herbs, potting them instead of planting them directly in the soil is completely sensible and may be even desirable. Because it is also easier to clear weeds from around potted plants compared to from the open soil.
