Apart from the claimed increase in download (and presumably also upload) speeds, what might the benefits be?
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We generally get around 14Mb/s download and 1Mb/s upload, checked with BT Wholesale speed checker, 'though do get the occasional brief slowdown.
What advantages might I get from switching to fibre - is it a more reliable platform? IS there less of a slowdown during times of high contention?
In theory*, there's no loss of signal strength over fibre regardless of line length, whereas the signal deteriorates very quickly on a long copper line. Thus if you get 100mbps at the exchange, you should get 100mbps at the end of a fibre line from the exchange. Any deterioration in speed will be in the final bit of copper between the cabinet and your house.
Thus, the difference to your connection speeds with FTTC will depend to a large extent how far you are from the exchange. We're six miles from the exchange so when we were on copper all the way, we were lucky to get 0.5mbps download speed. Since they upgraded the cabinet to fibre, our download speed is much improved, but we're still a mile from the cabinet so it's nowhere near as good as it could be - though we do now get a fairly reliable 17-20mbps download. Upload is still rubbish.
Recently, Openreach have been installing new cabinets along our road, so there is now a cabinet packed with fibrous goodness less than 200m from our house. In theory, we should be getting superwhizzyfastinternets very soon, but I don't know if/when they plan to hook us up to the new box (we've got our ISP on the case but unfortunately it's not as simple as just asking nicely).
*I'm sure someone more knowledgeable than me will be able to confirm/deny this. I suspect that in real life applications, there are losses over fibre.