One of the most interesting differences as outlined in the above-linked article of Berzin:
Mind as a Buddha-Nature Trait
Mind (mental activity) is a nonstatic phenomenon, in the sense that it changes from moment to moment because it takes a different object from moment to moment. According to the non-Gelug traditions, mind is a static phenomenon, in the sense that its conventional nature, as clarity and awareness, has no beginning or end, does not arise anew each moment, never changes, and is unaffected by anything. No matter what object mind cognizes, the conventional nature of mind remains the same.
The conventional nature of mind (mere clarity and awareness) is an evolving family trait (rgyas-‘gyur-gyi rigs, evolving Buddha-nature trait), not a naturally abiding family trait (rang-bzhin gnas-rigs, naturally abiding Buddha-nature trait). It evolves to become a Jnana-dharmakaya, an omniscient mind of a Buddha. The deepest nature of mind (its voidness of true existence) is a naturally abiding family trait. “Naturally abiding” means that it does not change; it does not evolve or develop through stages into the Corpus of a Buddha (Buddha-Body). It merely accounts for a Corpus of a Buddha – specifically, the voidness of the mental continuum accounts for the Svabhavakaya (the voidness of the omniscient mind) of a Buddha. The non-Gelug traditions assert that mere clarity and awareness is a naturally abiding Buddha-nature trait. It accounts for a Jnana-dharmakaya (the omniscient mind of a Buddha).
In order to ensure my mind never comes under the power of the self-cherishing attitude,
I must obtain control over my own mind.
Therefore, amongst all empowerments, the empowerment that gives me control over my mind is the best,
and I have received the most profound empowerment with this teaching.