Different clock speeds and slightly different cooler.
The G1 is probably worth that extra bit more, but if can save up and put a bit more into your budget you should be able to grab an RX 480 cheap when the 500 series refresh launches.
...there are actually 5 other "Gigabyte GeForce GTX 1050Ti"s (not sure which among these are you comparing with the G1 model:
Gigabyte GeForce GTX 1050Ti D5 (P/N: GV-N105TD5-4GD) Core Clock Speed: 1290MHz (1316MHz OC) to 1392MHz (1430MHz OC) | PCIe Power Connectors: None Size: L172 x W113 x H30mm | Cooling: 90mm (Single Fan) with No Heat Pipes | Backplate: None Lighting: None | Outputs: 1x DVI-D (DL), 1xHDMI v2.0b, 1x DP v1.4
Gigabyte GeForce GTX 1050Ti OC (P/N: GV-N105TOC-4GD) Core Clock Speed: 1316MHz (1341MHz OC) to 1430MHz (1455MHz OC) | PCIe Power Connectors: None Size: L191 x W111 x H36mm | Cooling: Windforce 2X80mm (Dual Fan) with No Heat Pipes | Backplate: None Lighting: None | Outputs: -Same as GTX 1050Ti D5-
Gigabyte GeForce GTX 1050Ti OC Low Profile (P/N: GV-N105TOC-4GL) Core Clock Speed: 1303MHz (1328MHz OC) to 1417MHz (1442MHz OC) | PCIe Power Connectors: None Size: L167 x W69 x H37mm | Cooling: (Single Fan) with No Heat Pipes | Backplate: None Lighting: None | Outputs: 1x DVI-D (DL), 2x HDMI v2.0b, 1x DP v1.4
Gigabyte GeForce GTX 1050Ti Windforce (P/N: GV-N105TWF2-4GD) Core Clock Speed: -Same as GTX 1050Ti D5- | PCIe Power Connectors: 1x 6-pin Size: L229 x W118 x H40mm | Cooling: Windforce 2X 90mm (Dual Fan) with 1xHeat Pipe | Backplate: Yes Lighting: None | Outputs: -Same as GTX 1050Ti G1 Gaming-
Gigabyte GeForce GTX 1050Ti Windforce OC (P/N: GV-N105TWF2OC-4GD) Core Clock Speed: 1328MHz (1442MHz OC) to 1354MHz (1468MHz OC) | PCIe Power Connectors: 1x 6-pin Size: -Same as GTX 1050Ti Windforce- | Cooling:-Same as GTX 1050Ti Windforce- | Backplate: Yes Lighting: None | Outputs: -Same as GTX 1050Ti G1 Gaming-
All the above cards (including the G1) are similar in terms of Memory Clock (~7008MHz), Memory Size (4GB), Memory Type (GDDR5), Memory Bus (128 bit), and Card Bus (PCIe3.0 x16).
So, if 10 Euros is not a big deal for you, the slightly upgraded features compared with the other 5 iterations of the Gigabyte GTX 1050Ti may be worth it.