I also did a back to back test on Speedtest and Broadbandspeedchecker. I found Broadbandspeedchecker gave ping times about ten times as big as Speedtest. Also the upload speeds were completely crazy on Broadbandspeedchecker, i.e. about five times as big as my link is capable of. The download speeds were similar to Speedtest. I would tend to trust Speedtest.
Until recently I was on a 24 Mbps contract that gave a real download speed around 10 Mbps. I upgraded to a 30 Mbps contract because it was virtually the same price. I didn't really expect a big difference since I am about 300 m from the exchange and there is certainly no box anywhere near my house to upgrade to fibre so the last 300 m would still be on the same copper cables. In fact the download speed has doubled to around 20 Mbps and the upload speed has more than quadrupled from around 0.5 Mbps to over 2 Mbps, which should help Skype video calls. The ping has lengthened slightly from 22 to 28 ms.