Yes, it does make a difference... but it depends very much on the length of the cable.
For short runs of 1-5m... you will be hard pressed to find any difference in speed... at least up to 1gbps speed.
For a 20m cable, I found the cheap cable would cap out at around 800mbit. I got a decent quality thick-walled cable (although not shielded) and that easily meets the full 1gbit speed.
How they run next to power cables and the shielding in the cable / quality & thickness of the copper used will make a difference... so it really depends on:
- Length (10m+ it might be worth thinking about)
- Shielding if it runs around lots of power cables
The only other thing to really think about is the quality of the interconnects... the bits that actually connect to the PC/switch/router can be absolutely terrible on cheap cables and break very easily. More expensive ones usually come with better quality connectors, which is worth a bit more.