The historiographical debate about the medieval origins of modern science is a long one (Duhem, Crombie, Koyré) but modern science (from Galileo on) is not at all aristotelian.
Modern science is based on mathematics and experiments. Aristotle was a great observer (in botany, zoology) but observation is not experiment.
And mathematics is absent from aristotelian and medieval physical science.
Is his [Aristotle] conception of "science" (certain knowledge through causes) different than the modern conception of science?
Certainly! The aristotelian ideal of science is the deduction of the explanation of natural facts from certain principles involving the causes of the said facts.
When Newton states the gravitation laws, he assert a mathematical law governing the behaviour of planets in motion subject to the action of a central force. He is not able to find an explanation based on the "cause" of gravitation (i.e.what is the force acting on the planets in motion) and he refrains to do so.
Newton celebrated statement : "Hypotheses non fingo" (Latin for "I feign no hypotheses") is a famous phrase used in the General Scholium to the second (1713) edition of the Principia :
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. [from I.Bernard Cohen and Anne Whitman's 1999 translation - see Wiki]
As you can see from my answer to a previous post I'm a "pluralist" and not an "essentialist" about science: science is a complex human activity, too complex to be defined with a single (essential) characteristic, and the same for the "scientific method".
Science is both botany and quantum mechanics; to do botany we need herbals and not mathematics. Aristotle and Albertus were good (very good, indeed) "empirical observers"; thus, they made a lot of observations and discoveries regarding zoology and botanics.
But physical science, as "invented" by Galileo and Newton, is mathematically and experimentally based : to build aircraft, nuclear fission and space travel (i.e.all the good and bad things that scientific knowlede gave us in 500 years), curiosity, enduring observation and "Aristotelian method" were not enough.
Suggstions for further readings regarding the debate about medieval and modern science
1) About the aristotelian method, the medieval origins of modern science and the "new" science .
John Herman Randall, Jr., The School of Padua and the Emergence of Modern Science (1961)
Alistair Cameron Crombie, *Robert Grossteste and the Origins of Experimental Science, 1100-1700, 1953
Alistair Cameron Crombie, *Augustine to Galileo: The History of Science A.D. 400 - 1650  (Revised ed. 1969)
Alexandre Koyré, Études galiléennes, 1939 (engl transl: Galileo Studies, 1978)
Alexandre Koyré, Études d’histoire de la pensée philosophique,  (3e éd. 1990)
3) Renaissance debate on the method
Walter Ong, Ramus, Method, and the Decay of Dialogue: From the Art of Discourse to the Art of Reason, 1958
Paolo Rossi, Francis Bacon: from Magic to Science, 1968 (ed or.1957)
4) About Galileo:
Stillman Drake, Galileo at Work, University of Chicago Press, 1978
Stillman Drake, Essays on Galileo and the History and Philosophy of Science, Volume I, University of Toronto Press, 1999
William A. Wallace, Galileo and his Sources. The Heritage of the Collegio Romano in Galileo's Science, Princeton University Press, 1984
William A. Wallace, Galileo's Logic of Discovery and Proof: The Background, Content and Use of His Appropriated Treatises on Aristotle's Posterior Analytics, Kluwer, 1992
5) Recent overviews on the "scientific revolution* :
H. Floris Cohen, The Scientific Revolution: A Historiographical Inquiry, University Of Chicago Press, 1994
Steven Shapin, The Scientific Revolution, University of Chicago Press, 1996
Edward Grant, The Foundations of Modern Science in the Middle Ages: Their Religious, Institutional and Intellectual Contexts Cambridge UP, 1996
Peter Dear, *Revolutionizing the Sciences: European Knowledge and Its Ambitions, 1500-1700 *, Princeton University Press, 2001
John Henry, The Scientific Revolution and the Origins of Modern Science, Palgrave Macmillan, 2008
Stephen Gaukroger, The Emergence of a Scientific Culture: Science and the Shaping of Modernity 1210-1685, Oxford UP, 2009.