weitaus
far
Used to intensify a comparison and means 'much' or 'significantly'.
Diese neue Methode ist weitaus effizienter als die alte.
This new method is far more efficient than the old one.

far
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far
Used to intensify a comparison and means 'much' or 'significantly'.
Diese neue Methode ist weitaus effizienter als die alte.
This new method is far more efficient than the old one.

'Weitaus' (far) is almost always used to intensify an adjective or adverb in the comparative form. It stands directly before the comparative word.
Ein Elektroauto ist weitaus leiser als ein Benziner.
An electric car is far quieter than a gasoline-powered car.
Do not use 'weitaus' (far) with the basic form of an adjective. A sentence like 'Das ist weitaus gut' (That is far good) is wrong. There must always be a comparison, so: 'Das ist weitaus besser' (That is far better).
Die zweite Version der Software ist weitaus stabiler als die erste.
The second version of the software is far more stable than the first.
'Weitaus' (far) is somewhat more elevated stylistically and expresses stronger emphasis. It is frequently used in written language and in more formal contexts to indicate a large difference.
Die tatsächlichen Kosten waren weitaus höher als erwartet.
The actual costs were far higher than expected.
much / a lot
'viel' and 'weitaus' can be very similar in comparisons. Both intensify the difference, for example 'viel besser' (much better) and 'weitaus besser' (far better). 'viel' is more general and very normal in everyday speech. 'weitaus' is used almost only before a comparative, and it sounds somewhat stronger or more elevated. Outside of comparisons, you cannot use 'weitaus' like 'viel': you say 'viel Arbeit' (a lot of work), but not 'weitaus Arbeit'.

Diese Route durch den Wald ist weitaus kürzer als der Weg an der Straße.
This route through the forest is far shorter than the road route.
Im Sommer habe ich zu Hause viel weniger Strom verbraucht.
In the summer, I used much less electricity at home.