What differences are there between CiviCRM 4.6 and 4.7?
The performance improvements to move from 4.6 to 4.7 when you have a large installation is, in itself, worthwhile (we did it when we had about 500k contacts, we would have done it earlier if we'd known how much faster some things were). If you go for a big upgrade, I recommend you to move to php7 too.

As for the features, this blogs list a few, but it's more than a year old. 

Since January last year, the bunch of the new features and developments have happened on 4.7, both in the core and in extensions. Whatever need or problem you are, it's way more likely someone else has already sorted it out or is working on it in 4.7, not in 4.6.

And in any open source project, being where the community is is in itself a good reason enough to go through a major upgrade.