Cave Man is right ( if not a bit partial ) 
The mini uses all Laptop components allowing it to be very quiet and power efficient. However this comes at a cost. The mini has a higher price is largely due the components just costing more then their desktop equivalents.
The performance is hindered somewhat by a laptop grade system bus and slower/smaller hard disk. Consequently it's not for everyone. Thats said the real world responsiveness will be at least equal to the PC you listed.
But for me the noise level and power requirements are very important since I have it running 24/7. At 14 these thing probably don't matter to you, but the power efficiency will more then recover the increased cost over 2 years.
The mini uses all Laptop components allowing it to be very quiet and power efficient. However this comes at a cost. The mini has a higher price is largely due the components just costing more then their desktop equivalents.
The performance is hindered somewhat by a laptop grade system bus and slower/smaller hard disk. Consequently it's not for everyone. Thats said the real world responsiveness will be at least equal to the PC you listed.
But for me the noise level and power requirements are very important since I have it running 24/7. At 14 these thing probably don't matter to you, but the power efficiency will more then recover the increased cost over 2 years.