There are two types of non-nuclear submarines. First is regular old diesel-electric. The next however is new and is called AIP. Air Independent Propulsion. In this form of propulsion, energy is stored in fuel cells like the german type 212 or in other methods like on Sweden's Gotland class. The German AIP submarines are said to be some of, if not the quietiest submarines in the world. They can stay submerged for over 2 weeks. That is about the best you can get for a non-nuclear submarine. As far as the Astute, it is designed to take on long range missions. American Nuclear submarines comparable to the Astute can stay submerged for 90 days at most. The Astute can probobly do this as well. The great thing about the Astute however is that its nuclear reactor doesn't need to be refuelled for 30 years, its entire service life. Usually nuclear reactors have to be refueled once every 15 years of a 30 service life. These refuels take a long time and are very costly. The Astute class can be compared to the Virginia class subs of the U.S. Both subs carry about 38 torpedoes and missiles. The are launced from vertical launch tubes. The Virginia class however has been designed to conduct littoral operations, or operations near the coast, as well as blue water missions and power projection. The Astute however is not designed for littoral operations. The Virginia, Astute and Seawolf classes are my favorite in the world. They are the quietest and deadliest subs out there. Yet they are very expensive with the Virginia and Seawolf classes costing $2 billion per sub.
