joojaa's guess is correct: C4D saves PSD with lossless compression, but TIFF without any compression.
The lossless compression in the PSD case is the standard method, which is fast but not super-efficient in terms of space savings. Adobe's docs only claim about ⅓ savings, whereas an algorithm like PNG can shave ½ or more off the size of a file, at the cost of some additional compression and decompression time.
There are similar compression methods available for TIFF — LZW and Zip — but for historical reasons, a lot of programs that read TIFFs only support uncompressed TIFFs. Consequently, many programs that write TIFFs don't even offer the option to compress TIFF output. This is what's going on with C4D in this case.
(Others, like Photoshop, include TIFF compression but turn it off by default, for the same reason.)
The actual image content of the resulting rendered frames should be the same in both cases, even when you're doing something tricky like multi-pass renders with all the layers and alpha channels for each frame set to go to layers in a single file, rather than separate files for each pass. C4D can use either TIFF or PSD for this purpose.
I would choose TIFF over PSD purely based on file format support in the app I was going to open the frames in after rendering. If that "next" app is Photoshop or After Effects, by all means, use PSD. If your app of choice won't read a layered PSD but will read a layered TIFF, C4D makes that option available to you. Or, you might choose instead to go the traditional route, and render each pass to a separate file, then use a compositor to assemble the passes into finished frames.
Adobe has been the custodian of the TIFF format ever since they bought Aldus, many years ago. They have since extended TIFF so that it supports many things you might think of as PSD-only, such as layers. So, even though C4D supports more PSD file format features than most other non-Adobe programs, it also does the same for TIFF.
If you aren't doing tricky things like multi-pass renders or separate compositing passes, you might want to think about using something like PNG for your rendered frames. If you can live with PNG's limitations as compared to TIFF — or PSD for that matter — it will save a considerable amount of disk space with no quality loss over PSD.