It is possible, but it depends on the ISP(s).
If you are getting 15Mbt sync out of ADSL then you'll not get less out of FTTC as the amount of copper involved is going to be a lot less.
If you are switching from ADSL2+ to FTTC
with the same ISP (and that ISP uses BT/OR's infrastructure for ADSL - LLU may complicate things a little) then you are going to see at least as good performance at all times. Your data is still moving between the exchange and the ISP by the same route and will be pushed around the ISPs network and peering arrangements the same way - all that is changing is the bit between you and the exchange.
If you are switching ISPs then it depends on the quality of the destination ISP.
If you did get lower throughput via FTTC and the problem was congestion within OpenReach's infrastructure then you would be getting the same reduced throughput if you were still on ADSL2+ (assuming, again, that LLU arrangements are not relevant to the discussion).
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Current ISP: Andrews & Arnold (AAISP) via FTTC at ~40Mbit down (has occasionally dropped to ~36) & ~10Mbit up, joined July 2011.
Previous setup: Be Pro with UploadPlus (ADSL2+, AnnexM), 12ish Mbit down, 1.6 up, happy customer for ~2.5 years.