Features Key features of the Galaxy Grand  vs Core 

screen size

If screen size or dual-SIM support aren't deal-breakers in your book, then the Samsung Galaxy S II is an excellent alternative.
Galaxy Grand | by GSM Arena (Feb, 2013)

screen resolution

Galaxy Grand
800 x 480
Galaxy Core
960 x 540
One huge knock against stretching such a low resolution along this much screen estate is the pretty low pixel density - 187 ppi to be exact.
Galaxy Grand | by GSM Arena (Feb, 2013)

memory

processor

Galaxy Grand
Dual core
Galaxy Core
Dual core
The Grand features the same dual-core 1.2 GHz Broadcom chipset.
Galaxy Grand | by GSM Arena (Feb, 2013)

camera resolution

Above the display you can see the earpiece, a couple of sensors and the 2 megapixel front facing camera, which can do video-calls.
Galaxy Grand | by GSM Arena (Feb, 2013)

Differences What are the advantages of each

Front view of Samsung Galaxy Grand

Reasons to consider the
Samsung Galaxy Grand

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Is 4G Yes vs No Somewhat common; Supports the fastest, most reliable networks
Acts as a wi-fi hotspot Yes vs No Somewhat common; Share your cellphone's data plan with other devices
Higher resolution front camera 8 MP vs 5 MP 60% higher resolution front camera; Video chat with other people
Bigger screen 5" vs 4.5" More than 10% bigger screen
Back view of Samsung Galaxy Core

Reasons to consider the
Samsung Galaxy Core

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Supports NFC Yes vs No Somewhat common; Enables payment by phone and other wireless communications
Much better theoretical download speed 150 Mb/s vs 21.1 Mb/s More than 7x better theoretical download speed; enjoy lightning fast downloads on modern networks
Records higher def video 1920 x 1080 @ 30 fps vs 1920 x 1080 @ Unknown 30x higher def video
Sharper screen 244 ppi vs 186 ppi More than 30% sharper PPI; enjoy photo-realistic, crisp images

Specifications Full list of technical specs

screen

Galaxy Grand  vs
Core 
Size 5" 4.5"
Resolution 800 x 480 960 x 540
Multitouch Yes N/A
PPI 186 ppi 244 ppi

hardware

Clock speed 1.2 GHz 1.2 GHz
Number of cores Dual core Dual core
RAM 1 GB 1 GB
Internal storage 8 GB 8 GB
Supported card formats
SDXC
SDHC
SD

photo & video

Camera 8 MP 5 MP
Resolution 8 MP 5 MP
Flash Yes Yes
Secondary camera 2 MP 0.3 MP
Video resolution 1920 x 1080 @ Unknown 1920 x 1080 @ 30 fps

cellular

Generation 4G 3G
Networks
GPRS (0.01 Mb/s)
HSUPA (5.76 Mb/s)
UMTS (0.38 Mb/s)
LTE Cat4 (150 Mb/s)
LTE Cat 4 (150/)
HSPA (unspecified)
EDGE (0.38 Mb/s)
Unknown (21.1 Mb/s)
LTE Cat3
HSDPA+ (21.1 Mb/s)
GSM (0.01 Mb/s)

battery

Capacity 2,100 mA·h 2,100 mA·h

form factor

Galaxy Grand  vs
Core 
Thickness 9.6 mm 9.8 mm
Size 76.9 x 143.5 x 9.6 mm 66.3 x 132.9 x 9.8 mm

sensors

Has an assisted GPS Yes Yes

music

Supports FM radio Yes Yes

software

Operating system Android 4.2.2 Android 4.2.2
Multitasking Yes Yes
App store Android Market Android Market
Adobe flash support No No
App store size 850,000 apps 850,000 apps

connectivity

Acts as a wi-fi hotspot Yes No
Supports NFC No Yes
Bluetooth Bluetooth v4.0 Bluetooth v4.0
Samsung Galaxy Grand
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Samsung Galaxy Core
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