The difference between a $1500 bike and a $2000 bike is generally that you will go from an aluminum frame with mid range components and entry level wheels to a carbon frame with entry level wheels and components. The carbon will be slightly lighter, but probably less stiff than the aluminum frame. The cheaper bike may actually feel livelier and faster than the more expensive carbon bike. Going from $2000 to $3000 will get you a stiffer carbon frame and mid range components. The stiffer carbon and better components will give the bike a sportier feel in general and make it feel more responsive to harder efforts. Going to $4000 will get you a ride-tuned stiff carbon frame to balance the stiffness with some better ride quality, with mid-range wheels and mid to upper range components. Going to the $6000 range will get you even lighter, mid-upper end wheels and electronic shifting.
In my opinion, the average new rider with less than 2 years riding under their belt will not be able to tell much of a difference if they were to ride the various bikes. The average rider who has been riding for a while but never does fast paced group rides or never rides hard just for the fun of it will notice the difference between a $1500 bike and a $3000 bike, but won't feel much difference between a $3000 and $6000 model. The slight differences in feel, response, and weight between the $3000 bike and a $6000 bike will really only be apparent to riders who push their bikes hard and who measure themselves against the clock or others riding hard in a group. A bike is just a tool, and what kind of tool is worth what kind of money to you depends on how you plan to use it.