I am about to purchase a new lawnmower, but i am in a quandry as to
which type i will buy, either petrol driven or electric. Can anyone
tell me whether there is a significant difference between these types,
with respect to grass cutting quality?

With corded electrics, you're hauling cord with you... can get heavy. With
battery powered, you've got low battery problems eventually. Either tend not
to do well with heavy, wet grass.

Gasoline engines are more expensive but easier over the long haul, imo.
They're good for large area cutting and heavy grass, but can be hazardous
because of the powered blades and mowing over various objects. They will
handle dense lawns and fairly long grass.

Two-cycle engines (where you mix oil and gas in a preset ratio, rather than
having separate oil and gas in the engine) are major air pollution causes.
Four-cycle engines are some better, but need tuning now and then.

The best cuts tend to come from reel mowers -- the old fashioned push mower,
rather than rotary blades, but they won't handle long grass very well, and
usually have fixed cutting heights. IMO, if the lawn is small enough for
an electric mower to handle, it's small enough for a people-powered reel mower
(assuming a healthy owner). Quieter, too.

Whatever you choose, keep the blade sharp and learn to mow properly -- timing is
very important.

Kay