For most small to medium gardens, an electric strimmer is perfectly adequate. They are lightweight, quiet and less expensive than their petrol counter-parts. However, unless you opt for a battery powered cordless strimmer the power cord will restrict movement in larger gardens.
For heavier work, or clearing large areas, a petrol driven strimmer or brush cutter is more suitable than an electical model. In addition to nylon cord, many can be fitted with different metal blades for tackling brambles, brush and small trees.
Multi purpose models can serve as hedge cutters, pruners, soil tillers and power brooms through the addition of various attachments. If you have a large garden to maintain, these models make perfect sense as you only need one engine to power a range of tools.
For really tough growth, consider a wheeled trimmer or a field and brush mower.
In general, petrol strimmers require more maintenance than electric strimmers.