Talktalk vs BT

Both my neighbour and I get our broadband via the 'copper wire' and both houses are fed from the same telegraph pole. I have used 4 different speed test sites on both of our laptops (mime is the newest and on windows 10) and my download speeds with Talktalk are over 2 Mbps slower than what my neighbour receives with BT

Entirely possible, as different ADSL2+ providers may run their hardware differently.

You need to look at the modems actual connection speeds, noise margin and attenuation figures if you want to understand it more