To my understanding impyramid expands or reduces image size by fixed factor of two while with imresize you can give arbitrary scaling factor. With imresize you can also select different interpolation methods while with impyramid that is fixed to given kernel...

But which is more efficient for upsampling? Suppose I want to upsample an image by twice it's size, which one should I use?

As always it is a trade off between quality and computation time. Also the target platform may have to be considered (ie embedded dsp/cpu/gpu/fpga tta/what ever...). On my desktop I get:

>> testResize %(here input 192x256x3)

pyramid time: 3.348ms psnr:32.22dB kernel = [14-a2,14,a,14,14-a2], where a = 0.375

imresize time: 1.555ms psnr:29.20dB kernel = nearest

imresize time: 1.553ms psnr:29.20dB kernel = box

imresize time: 2.442ms psnr:31.84dB kernel = bilinear

imresize time: 2.657ms psnr:31.84dB kernel = triangle

imresize time: 3.042ms psnr:31.93dB kernel = lanczos2

imresize time: 3.449ms psnr:31.95dB kernel = cubic

imresize time: 3.677ms psnr:31.92dB kernel = lanczos3

So if one wants fastest possible way one would select imresize with nearest, while cubic appears to give better quality and pyramid the best quality. However, also the contents of the images to be resized may affect how the kernels perform quality wise as well if the gpu is used and if the gpu supports for example HW filtering with given kernel (e.g they usually do with bilinear).

I really would encourage to write own test scripts when figuring out problems like this, so that one can be sure that the own requirements are met. To see how easy that is see the attached test script...