Let's assume we will only care about the hydrographs and time step of model operation and data temporal resolution are same. 

It depends on the drainage area.

For a specific basin, there is a temporal scale  over which long time step (data resolution) will change calculated hydrograph significantly. Qualitatively, the large the basin, the longer this temporal scale.

For a basin of 100km^2, 5 min or 60 mins will not make large diff. However, for a basin of 1 sq. km, they will.

Apart from the drainage area, there are some additional impact factors that are very important to the selection of computational time step.

The selection of computational time step of rainfall-runoff simulations is mainly determined by the hydro-meteorological and geophysical characteristics of the study catchment. These impact factors produce mainly two kinds of runoff generation mechanisms including the so called "saturation excess" and "infiltration excess".

Saturation excess mechanism usually describes the runoff generation process of humid and semi-humid regions. Infiltration excess mechanism is suitable to the runoff generation process of arid regions.

For saturation excess runoff generation, the runoff computation results is usually insensitive to the rainfall intensity. Therefore the computational time step can be relatively larger, such as 60 mins, one day or even one month.

For infiltration excess runoff generation, the generated runoff is very sensitive to the rainfall intensity. Therefore, the computational time step must be small (such as less than 10 mins) to ensure a reliable and stable simulation accuracy.

The appropriate temporal resolution of a hydrological model will indeed depend on hydroclimatological and geophysical characteristics. This means for instance that for large and slowly responding catchments you can work with a coarser temporal resolution than for a small and quickly responding catchment. If one would have a temporal autocorrelogram of the runoff (if that's the variable of interest), one could estimate the appropriate temporal resolution of the rainfall-runoff model (see for instance the two publications below).

Furthermore, the appropriate temporal resolution will obviously also depend on the aim of the study (high flows, low flows, water balance study etc.) and the availability of data. There should always be a balance between data availability, study aim and model complexity (including spatial and temporal scales).

Article Determination and integration of appropriate spatial scales ...

Article Appropriate scales for hydro-climatological variables in the...

I concur with all the previous answers. I have two more: the objective of your modeling study and the model you are using.

1. Is this for a water supply study for which total volumes of water at a daily or monthly time step are necessary or a flood protection study where accurate knowledge of peak discharge and stage is necessary? Will the model be used for exploratory or planning purposes (coarser temporal scale may be sufficient) or for regulatory purposes (a smaller time step is necessary).

2. Depending on the model you are using, iterative resolution of differential equations may cause computational convergence issues that will drive the choice of the time step.

Besides other comments I fully agree with that of Kevin. There is a need to consider groundwater input to your basin in regard of base-flow, Mainly the response in your stream resulting from far away rainfall before you do any modelling, Do get from Mexico saludos,jjoel carrillor

Dear Experts 

Thanks for your constructive and informative suggestion. Further to this, I would like to know is the above theory also valid in the mountainous catchment.

Dear Vikram, thanks for your comment. Of course, as far as science is concerned, you will have to find the boundary contdtions validating your views on why in your particular basin, such conditions are unvalid. That means you must, sample (surface and groundwater), analize (chemistry and Isotopes),  measure (runoff response), inteprete within the 3D geological framework, consider vertical groundwater flow, etc 

Thanks everyone for your comprehensive answers, I really appreciate the help

The finer the better!

It is really a good string of discussion. I would like to add a bit here to invite suggestions/inputs from learned expert here.

"Is there any practical significance and use of having rainfall hyetograph and runoff hydrograph , both at time step of 1 day; even if catchment is large enough ?" If so please provide some good references/links.

Interesting question,and thank you for all your answer