They are very different robots with very different goals, so it should be no surprise that the G1 appears much more agile.
some specs here: https://www.unitree.com/H2
claimed 3h battery life, can hold about 10% of its weight (7kg, with arms)
Unitree's demos are a lot of fun, and the antics of releasing the G1 to the public has certainly captured people's attention, but a "working" robot won't look, act, or develop from the G1 or even H2.
My point was that BD could probably build a robot with the shown acrobatic capabilities, but they choose not to because their goal is to build robots that carry heavy loads for industrial applications.
Focussing on load capacity is missing the forest for the trees
The fact that Unitree's robots appear so acrobatic reflects that they are likely on par with BD in terms of capabilities but have a different target market.
Human individual fingers can withstand internal loads of hundreds of newtons, (possibly a thousand for brief periods if you're a star rock-climber), while at the same being capable of tasks such as writing, which require high speeds and (sub-)millimeter precision, while also enjoying 4 degrees of freedom (5 for the thumb), and they're stuffed full of sensory organs to boot. Oh and they're also self-healing, so taking some damage during use is no problem and they will actually adapt to the task they're used for over time. Everything we can make compared to this is laughably primitive.
If you make an agile robot big, it now weighs more, which means its joints now need to handle greater loads, which makes it necessary to make them much bulkier and heavier.
A lot of this is just inherent limitations of electric motors and having to convert rotational energy. This gets heavy fast.
Decent synthetic electrically-driven muscle fibers would go a long way.
I personally agree with the rest, recommend you remove that last bit about downvoting and sneering if you can still edit