Do you have the part numbers of the two Op-Amps?
Generally Rail to Rail signifies that the device will operate with signals from the minus power supply all the way to the Plus power supply connection.
Some devices do not operate correctly when the signal is within a volt or two of either supply connection.
Rail-to-Rail becomes much more important when you are running a circuit on battery voltages at 5V or below.
For example, suppose you are doing something with a PIC running on 5V. You want to amplify a sensor signal so that you can feed it to the A/D converter in the PIC. To utilize the full dynamic range of the A/D converter (0-5V), you have to amplify the sensor signal so that it ranges from near 0V to near 5V. A rail-to-rail CMOS OpAmp will do that; while a old BiPolar OpAmp wont even come close. A 741 wont even operate on 5V,
Let it be known that there's no such thing as a rail-to-rail op-amp. There'll always be some voltage loss which will always increase with the output current and at lower supply voltages. The datahsheet will give you the saturation voltage at different output currents and supply voltages.
As MikeMl implied, Rail-to-Rail op amps are useful for any single supply requirement since the the input and output can operate to ground at the input and output (within the limitations noted by H999 for the output). A normal (non Rail-to-Rail) op amp with a single supply can typically only operate to within a volt or two of ground.
From the discussion, I think that the conclusion is:- i should use rail-to-rail op-amp when amplifing a small signal of range in mv. Also this can be used when working with the negative polarity signal.
While a bi-polar op-amp can be used while working with large signals.
I would say it like this: You should use a rail-to-rail opamp whenever you want the signal at its output (regardless of how small the input is) to vary from (Vss+a few mV) to (Vdd-a few mV).
If an output range from (Vss + a couple of V) to (Vdd - a couple of V) is sufficient, then you can use a non-rail-to-rail opamp.
Note: Vdd is connected to the Positive supply; Vss is connected to the Negative supply if split-rail or ground if single-rail.
As MikeMl implied, Rail-to-Rail op amps are useful for any single supply requirement since the the input and output can operate to ground at the input and output (within the limitations noted by H999 for the output). A normal (non Rail-to-Rail) op amp with a single supply can typically only operate to within a volt or two of ground.