Which computer is best for RECORDING AND PLAYING Minecraft?

1st computer, price: $1300

Specs:Details:
Warranty Terms - Parts1 year limited
Warranty Terms - Labor1 year limited
Height19 inches
Width8 inches
Depth20.5 inches
Weight32 pounds
Processor BrandIntel®
ProcessorIntel® 4th Generation Core™ i7
Processor Speed3.7GHz (with Turbo Boost up to 3.9GHz)
Cache Memory10MB on die Level 3
System Memory (RAM)16GB
System Memory (RAM) Expandable To128GB
Type of Memory (RAM)DDR3 SDRAM
GraphicsNVIDIA GeForce GTX 660
Video Memory2GB (dedicated)
AudioHigh-definition 7.1-channel surround sound
SpeakersNone
Network CardBuilt-in 10/100/1000 Ethernet LANAllows a computer to connect to a network either by using cables (Ethernet) or wireless technology (IEEE 802.11).
Wireless NetworkingNone
Recordable DVD DriveYes, double-layer DVD±RW/CD-RWDrive that can read CDs and DVDs, as well as write and rewrite CDs and various types of DVDs.
Recordable DVD Drive SpeedsDrive speeds not specifiedMaximum write (DVD±R), rewrite (DVD±RW) and read (DVD-ROM) speeds of the DVD±RW drive.
Direct-Disc Labeling No
Digital Media Reader or SlotsNo
Available Expansion BaysExternal: 6 (5.25"); Internal: 2 (3.5")
Available Expansion Slots4 PCI Express x16, 1 PCI Express x1, 4 DIMM
USB 2.0 Ports3 USB 3.0 (1 front, 2 rear); 8 USB 2.0 (2 front, 6 rear)Ports that allow high-speed (up to 480 Mbps) data transfer between compatible devices.
Keyboard DescriptionUSB
Other Control Devices (mouse, etc.)USB mouse
Operating System PlatformWindows
Operating SystemWindows 8
ENERGY STAR CertifiedNo
Best Buy PC AppNo
HDMI OutputYes
Blu-ray PlayerNo
Graphics ChipNVIDIA
Drive Capacity2TB
Discrete GraphicsYes
Gaming SeriesYes
Hard Drive Size2TB
Hard Drive TypeSATA III (7200 rpm)
UPC892167017218

2nd computer, price: $550

Specs:Details:
Warranty Terms - Parts1 year limited
Warranty Terms - Labor1 year limited
Height19.1 inches
Width8 inches
Depth16.8 inches
Weight32 pounds
Processor BrandAMD
Processor PlatformAMD VISION FX
ProcessorAMD FX-Series(Also known as the CPU).
Processor Speed3.8GHz (with Turbo CORE up to 4.0GHz)
Cache Memory4MB on die Level 2
System Memory (RAM)8GBT
System Memory (RAM) Expandable To16GB
Type of Memory (RAM)DDR3 SDRAM
GraphicsNVIDIA GeForce GT 610
Video Memory1GB
AudioHigh-definition 5.1-channel surround
SpeakersNone
Network CardBuilt-in 10/100/1000 Ethernet LAN
Wireless NetworkingNone
Recordable DVD DriveYes, double-layer DVD±RW/CD-RW
Direct-Disc LabelingNo
Digital Media Reader or SlotsNo
Available Expansion BaysExternal: 2 (5.25"), 1 (3.5"); Internal: 4 (3.5"), 1 (2.5")
Available Expansion Slots1 PCI Express x1, 2 PCIFor digital cameras and digital audio players:
USB 2.0 Ports6 (2 front, 4 rear)
Keyboard DescriptionUSB gaming
Other Control Devices (mouse, etc.)USB gaming mouse
Operating System PlatformWindows
Operating SystemWindows 8.1
Operating System Bit Version64-bit
ENERGY STAR CertifiedNo
Best Buy PC AppNo
HDMI OutputNo
Blu-ray PlayerNo
Graphics ChipNVIDIA
Drive Capacity1TB
Discrete GraphicsYes
Gaming SeriesYes
EPEAT QualifiedYes
Hard Drive Size1TB
Hard Drive TypeSATA III (7200 rpm)
UPC892167013333

The first one, that one is more than good enough in fact the top one will be good enough for recording and playing higher end games like BF4, Crysis those type of games at medium-high even higher when not recording

They don't even compare. (i mean the price difference if obvious:/)

recording/live streaming is extremely cpu demanding so the better cpu, the better you will be able to do it while gaming.
gaming performance is dependent on your gpu.

a 4th gen i7 is easily enough to play any game and record or stream at 1080P w/o any lag at all.
the gtx660 should be capable of playing games on high settings at 1920x1080.
But its certainly not really worth $1300. You can build it yourself far cheaper.