Have you tried both resampling and reprojection? Did you also take into account that MODIS is in Sinusoidal projection and Landsat is in UTM projection? It may be a good idea to follow some research articles to see how others have carried out the same process that you are trying to accomplish. I have attached two relevant links that might be helpful. 

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140009137.pdf

http://landsat.gsfc.nasa.gov/pdf_archive/Wulder_2009_EMA_inv-landsat-modis.pdf

https://hexagongeospatial.fluidtopics.net/book#!book;uri=5d68e1db557af5bab494d96c7f8e1a9d;breadcrumb=5cd5bd6b4039c5ac47f0a21ea18e6507-197c04c83d9888670ab2ed6a2ab24a09-d671a5a50f151bdcac6a106552f9aabc

resample it by any software

http://web.pdx.edu/~jduh/courses/Archive/geog481w07/Students/Craver_Resampling.pdf

Hi Sumit, 

This is a good question and there are thoughtful reasons for following one way or the other resampling method using various interpolators such as Nearest Neighbor, Bilinear Interpolation and Cubic Convolution (check the pdx link attached by Firoz) depending on your purpose. I found a few links on the web that will be helpful. 

http://gis.stackexchange.com/questions/94302/when-dealing-with-rasters-of-varying-resolutions-should-one-resample-to-the-high

http://gis.stackexchange.com/questions/199397/resample-raster-to-lower-resolution

http://gis.stackexchange.com/questions/101483/how-to-resample-a-raster-to-higher-resolution-in-qgis

http://gis.stackexchange.com/questions/123989/convert-raster-resolution-in-arcgis

http://gis.stackexchange.com/questions/10234/resizing-image-resolution-from-1000-m-to-250-m-in-arcgis-desktop

http://euler.nmt.edu/~brian/upscalingpreprint.pdf

scaling transformation pixel size 30m to 250m.

http://www.sciencedirect.com/science/article/pii/S0273117703905448

Simply rescale your data using Rescale Tool in Erdas Imagine.

Thank you every one for your response.

Dear Firoz 

the 1st link you have attached is not accessible. The ppt was very useful for the understanding the details of the problem. I have  tried all these methods,but after resampling to 250 resolution  landsat image pixels doesn't fall directly upon the modis image pixels, as it is required to corelate pixel by pixel. can you please help me in this regard. Because of some problem in our lab I don't have erdas imagine now. please suggest me methods so that I can peform it in arcgis or envi or any free software.

I tried each and every option re-sampling in arc gis resize tool in envi but each of them produced the pixel size as required but these pixel doesn't overlay on each other as it is required 

Have you tried both resampling and reprojection? Did you also take into account that MODIS is in Sinusoidal projection and Landsat is in UTM projection? It may be a good idea to follow some research articles to see how others have carried out the same process that you are trying to accomplish. I have attached two relevant links that might be helpful. 

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140009137.pdf

http://landsat.gsfc.nasa.gov/pdf_archive/Wulder_2009_EMA_inv-landsat-modis.pdf

1st i projected the modis into the same projection system as landsat8 to utm zone 45N wgs1984 as per my location, then after i aplied the re sampling .

you have to do resampling of both data is same resolution. It is very easy to do on envi or erdas software. I hope you can get online video on YouTube. All the best. 

ERDAS software is good for resolution merging

Thank you so much to all for helping me out.

I got the solution to the problem,the paper on "Quality assessment of Landsat surface reflectance products using MODIS data sent by James Varghese" was the most useful which describes all that problems of alignment of pixel over each other in details. 

I thought that it might be help full for everyone

Basically the simple re-sampling of  image of modis to landsat resolution or vice versa will only re-sample into a required resolution but it would create a cell alignment problem as example if we re-sample the modis into 30m resolution then although the pixel size get reduced still the pixels of modis don't directly lie over the pixels of landsat8 . But  Snap Raster tool in the ARC GIS environment setting will adjust the extent of output rasters so that they match the cell alignment of the specified snap raster.

While re-sampling, the lower left corner of the extent is snapped to a cell corner of the snap raster, and the upper right corner is adjusted using the output cell size. As a result, when the output cell size is the same as the snap raster cell size, the cells in the output raster are aligned with the cells of the snap raster.  

Thanks Sumit for sharing the solution. Glad to hear the paper was helpful. Indeed 'Snap Raster' (Environment Setting) within ArcGIS is a possible solution. But I am sure there are other open source ways to achieve the same result.

http://desktop.arcgis.com/en/arcmap/10.3/tools/environments/snap-raster.htm

Yes maximum people told me to use the resize tool in envi I saw some video from the youtube. but dont know why but I could do that correctly. And as I don't have access to erdas so I could even able to try it out.

Resample the Landsat image of 30m to 250m resolution, then you can now make your comparison.

Dear colleagues. Only the 200km-central strip of MODIS is Landsat compatible. Another problem is that only the same orbits. Remember that on the west side it is later than on the east, that is the modis trap.

Dear Francisco,

I did not get your point exactly. Could you please elaborate it a little more. 

The point is that resampling will not enaught. We must consider illumination condition, must be use, then, the central stripe of modis.

Aldo, we must be carefully with slight spectral incompatibilities between some bands.

Also, another point is not compare Modis poduct with an image Landsat, one is a composite and the other is an image adquired in one date.

Sorry, I am not annoying person only I dont like modis.

Also, very sorry by spelling mistakes.

Hugs colleagues

Dear Dr Sumit Kumar Sahoo,

You can realize your idea by using ArcMap software