How powerful are today's telescopes compared to some of the first used to look at the heavens?
"Powerful" for a telescope can mean magnification or light gathering (amplification), and the answer to both is "a lot".
Telescopes do two things, make things look bigger (magnify) and make faint objects look brighter (amplify).
The magnification is mainly a function of the focal length, and the amplification, or light gathering, is a function of the aperture, or diameter of the scope.
Usually astronomers are more concerned with the aperture, wanting to gather more light from faint objects, rather than just increasing the magnification.
But to answer your question, two of the earliest telescopes were Galileo's and Newton's. Galileo had a lens-based (refracting) telescope with a focal length of 980 cm (0.98m), and an aperture of 37 mm.
Newton had a reflecting telescope with a 50 mm mirror and a focal length of 15.8 cm.
Today, there are a number of telescopes with an aperture of 10 m, and telescopes under construction with an aperture of 30m! And while those telescopes have fast focal rations (short focal length compared to diameter) some 20th century telescopes have focal lengths of more than 30 m; the largest telescope in Canada, at the David Dunlap Observatory, has a focal length of 34m.
Comparing these values to the original scopes mentioned above, the DDO scope has a focal length (intrinsic magnification) 37.7 times greater than Galileo's, and 215 times Newton's.
In terms of aperture, the Keck, 10m telescope has 40,000 times the light gathering ability of Newton's scope, and 73,000 times more than Galileo's!