Technically, catenary beats third rail hands down:
* Current collection is reliable at speeds exceeding 200mph. Third rail gets dicey above 80-90mph, and useless shortly after.
* Catenary allows higher voltages. Higher voltages mean lower losses. Third rail effectively means a sub station every mile. And even then, losses get really obnoxious at high current levels.
* The higher voltage means lower current. This means less arcing.
* You can't gap with catenary (unless you're Amtrak
* Third rail is vulnerable to leakage paths, and dirt. Garbage near the rail can easily start a fire. Unless the ROW is kept clean, fires happen a lot. It was a HUGE problem for the NYC/PC/Conrail in/out of GCT for many years.
* Third rail arcing can ignite the train. This actually has happened a few times with the LIRR's DM fleet.
* Locomotives on third rail are difficult because of the high current draw.
* Third rail sucks in the snow and ice.
* Substations are more numerous with third rail, and need to be built with special high speed breakers (due to the DC). In addition, fault currents can reach 6 figures, easily. Catenary running at commercial AC frequencies uses standard, off the shelf, breakers and protection relays. The substation designs aren't radically different from regular power systems.
I won't mention the obvious safety issues with third rail. And third rail cost a LOT more than catenary.
Oh yeah, and newer designed catenary systems are hardly intrusive - the New Haven's is because it was old, carried transmission lines, and spanned 4 tracks. Look at photos of Tumbler Ridge, BM&LP, recent European lines, etc. Or NJT's Coast around Red Bank.