I don't use either of these lenses, but I do have the Tamron SP AF 70-300 F/4-5.6 Di VC USD, which was the "go to" lens for Nikon 1 users who couldn't afford the Nikon 1 70-300mm, but this has been supplanted by the new AFP 70-300mm f6.3 DX nikkor which is probably the new "go to" lens.
There is a "lot" of information on the Nikon 1 forum at DPReview about what lenses work, and I am certainly aware of people using the 300mm f2.8 Nikkor with Nikon 1 (not sure why Nikon don't list it as compatible, as most Nikon lenses are). From memory I can't remember if the Tamron 70-200mm f2.8 has ever been mentioned. Whether third party lens works or not is a bit of a lottery, and can be broken with a firmware update.
Fred Glickner has an incomplete and out of date list of third party compatible lenses, which doesn't help you but may be useful to be aware of
http://nikon1user.blogspot.co.uk/2015/05/ft-1-third-party-lens-compatibility.html
If you can't get anyone here with practical experience of these lenses, I would have a look at the Nikon 1 forum on DPReview. Its one of the better DPReview forums.