Nick, let me provide you with the benefit of our experience as a manufacturer of Ethernet-over-coax devices (Veracity). We've been selling our range of HIGHWIRE adapters for seven years now (longer than anyone else in fact), and the installed base is now vast. These devices have been installed onto all sorts of coax cable types (RG59, RG6, RG11 + others) and all ages of coax and across several hundred meters of cable, depending on cable type (RG59 is the most limited, but should still give you 300m - although watch out for copper-clad steel coax if you want to transmit POE as well).
The feedback from our integrators is that in the vast majority of cases the old cabling works well and stays working. Typically if a connection is a bit iffy, re-terminating with new BNCs solves the problem. If the cables were getting any kind of useable analog signal across them before, then generally they'll give perfect performance for the digital transmissions. The thousands of HIGHWIRE installations which have been in for 5+ years and are still performing perfectly. In fact some installations have upgraded their cameras again since (from standard IP to mega-pixel IP), but just kept the EoC adaptors.
It's also possible to buy EoC adaptors for the camera end which have a built in switch, so you can run up to 4 Ethernet devices down a single coax - note that not all the devices need to be IP cameras - an extra Ethernet link can be very useful for other network connections sometimes.
Just be wary that the EoC solution you choose provides sufficient bandwidth for mega-pixel cameras, as there are low-cost solutions on the market with limited bandwidth. You need to be aware that even if a camera is running only say an average 2Mbps, the instantaneous bit rates can be many times that, and if the adaptors can't handle that, you'll see frame stutter and drop-outs, and it will be nothing to do with the cable.
I take Ari's point about the NYC MTA system, and we also have experience of underground transportation systems. These are not representative of normal industrial CCTV installations and indeed can be very difficult due to the length of the cables (up to 1000m sometimes), the cable types (often not 75ohm CCTV cable), their age (30 years + !) and condition (they've been in a very harsh environment for a long time). We do have special solutions for such applications, but that's not relevant here. Just don't be put off by such (very real) horror stories. Coax cable is an excellent and long-lasting transmission medium. Reusing it is smart, lower cost and environmentally sound.
Just a comment on HDcctv - whilst it doesn't require separate adaptors, these are built into the devices at each and you still pay for them. The flexibility of EoC versus HDcctv is that you can use any IP cameras - indeed any Ethernet signal at all. In another 5 years time, we expect that HDcctv will have faded away.
I hope you find the above useful.