The difference between cooking beef for stew and lamb for stew

In most of my recipes, I use the beef method because beef is more widely available in the U.S. where I am living right now.  To cook beef for stew, use the following technique:

•  Sautee beef cubes in olive oil, salt, pepper and spices until brown
  
• Add water
• Bring to a boil 
• Reduce heat to low and simmer covered until beef is cooked (45 min - 1 hour)

Lamb takes longer to cook so I use the following method

• Sautee lamb cubes in olive oil, salt, pepper and spices until brown
• Add water
• Reduce heat to medium and simmer covered for maybe 45 min
• Reduce heat to very low for maybe 10 min until meat is completely tender