TIFF files are bigger than PSD files. PSD files compress–granted, not as badly as JPEG, but compression is still there. “TIFF files are not as compressed (if you choose LZW compression) or aren’t compressed at all if you don’t compress them, and so are much larger, but contain the same information about the image they contain.” TIFF files are also best with images that are going to be shared, as they can be opened with different programs. PSD files do not have this benefit. [LINK]
One would think that with compression comes smaller files, but that’s where TIFF comes in to give one heck of a plot twist. “In many cases a TIFF image with LZW compression applied will be larger than the same TIFF image without compression applied. Yes, compression for TIFF images can actually make the file larger!” [LINK]
In terms of space, PSD is a great option, however it does have lossless compression. Choosing which one to apply to your images is more of a personal preference, seeing as both have their benefits as well as drawbacks.