let me setup the phone first then only slowly 'play' with u

now trying to migrate my whatsapp account to my new phone

Copy pasta the storage>whatsapp folder to your new device

Psn sorry for triple post, I'm on phone

backup your conversation from your old phone then paste the folder to nexus 5
make sure you are using the same number so that you restore back the backup
tried it and it display the same.
both in chrome

is like the text in nexus 5 is slightly larger than s3 but both in 100% zoom

paste to storage, the same directory where you copied it from
ie phone A/storage/whatsapp --> phone B/storage

IIRC every convo is in that folder already, after you install whats app on phone B, paste the folder, then only start up whatsapp, the app should detect and restore the convos
hmm... that i have no experience, sorry about that, maybe try with pictures? ie 3000x3000 pixel picture, open in chrome, zoom to 100%, should see more of the picture in  N5 compared to S3...