cheaper? no. it used to be in 300 USD range, while 1050 TI is close to 100. The reason for 680's cost is that it used to be top of the line card (see the last two digits, 80) and while old, people still ask relatively much for them.
Yes, raw power wise, 680 is bit better than 1050 but... if you have a low budget, go for 1050.
if you have that 300 to spend, get more recent card than 680, like 1060, it will be around 50% faster than old 680 for same cost or lower.
1050 TI vs 680, 680 is around 20% faster and cost 2.5 times more (250 to 300)
680 vs 1060, 1060 is around 50% faster and costs around same. (250 to 300)
so if you need to get a card at low price, 1050 TI is good choice
if you don't have as tight budget restraints, 1060 is decent alternative.
looking at youtube, people get AC unity to play at 30 to 45 FPS on ultra/high details with 1050 TI so it could fit your needs.