I think you can configure both to converge extremely fast, but if I had all Cisco routers, I would prefer EIGRP because of it's flexibility regarding the design. OSPF has it's own rules (area 0, filtering/summarizing only on abrs, etc.)
However, with OSPF ip ospf dead-interval minimal hello-multiplier 4 you can set 4 hellos per second (gives hello interval = 250ms), adjust dead timer to 1 second and you will have a pretty fast convergence. I don't know whether with EIGRP you can get under 1 second for a neighbor to fall.
In addition to previous answer, if EIGRP has a feasible successor route in it's topology table and the active route in the route table fails then it is almost instantenous in terms of failing over to the new route because EIGRP does not need to query any other routers or do any internal calculations, it simply installs the new route.
according to CiscoPress
EIGRP convergence time increases as more routes need to be processed. However, there is a far
bigger impact for networks with EIGRP feasible successors than for networks with no feasible
Subsecond timers are not available for EIGRP. experimentation suggests that
setting the EIGRP timer below 2 seconds can lead to instability. The recommended EIGRP
minimum timer settings are 2 seconds for hellos and 6 seconds for the dead timer. Subsecond
settings are not an option
Subsecond hellos are supported
DeadInterval-minimum 1 second
Hello multiplier is used to specify how many Hellos to send
within 1 second
if helpful Rate
Just to add.. to detect protocol neighbor failures and convergence, you can also look for BFD rather than tweaking protocol timers. By this detecting neighbor failures is independent of protocols and BFD is light weight than protocol packets.
There are two factors that determine convergence time. They are the time it takes to recognize a failure and the time that it takes to select a new route. There may or may not be differences between OSPF and EIGRP in detection and as mentioned there are things like BFD that can help improve time to recognize the failure. In terms of time to select a new route, if there is a feasible successor then EIGRP is faster than OSPF. If there is not a feasible successor then it is hard to know which is faster and it may very well depend on the topology of the network.
I would suggest that it may be more helpful to recognize that newer routing protocols (EIGRP and OSPF) converge more quickly and that older routing protocols (RIP or IGRP) converge more slowly.