To keep readers from confusion and to promote neutrality, the naming of these items in this post shall be "BLM events" and "Jan 6 event".
At the moment, technical data like number of participants and clear timeline of events is difficult to come by, but there are a few items that can be seen without that data.
There's one major difference that should be apparent: They're categorically different things. The BLM events are a broad group of events that spanned several months and hundreds of cities. The Jan 6 event is a single event. We usually call this a category error. When you try to compare a single item to a group of items, you can probably find single items from the group to make any comparison/contrast you'd like. Machavity's answer, for example, calls the BLM events "mostly peaceful", but leaves opaque what would make the singular Jan 6 event "mostly peaceful". Such metrics are inherently not comparable.
But, we can note where the Jan 6 event is totally unique, where even exceptional cases of the BLM events cannot compare.
The most obvious uniqueness of the Jan 6 event is time and place. The Jan 6 event involved the security breach of a politically significant building while politically significant happenings were taking place in that very building. To my knowledge, no such BLM event comes close to that.
The next difference might be argued by some, but to a plain definition the Jan 6 event involved persons who were entirely politically motivated. The BLM events had political overtones, but are better defined as socially or civilly motivated. Definitely the events were starkly supported by one political party and starkly rejected by the other, but no specific political person, process, etc was the focus of their gripes. Contrast that with the Jan 6 event, their gripe was a very specific political process centered around a specific political person (Trump). Again to my knowledge, no BLM event compares to this. There might be a few that come close, like the ones involving protesting outside a politician's home and demanding resignation.
Wanting to keep things neutral still, I must note that on the face of it, the above two items together look like insurrection, and certainly politicans on both sides have called it such. However, the handful of so called "autonomous zones" that came out as a result of BLM events are clearly in the same vein. I'm not sure if declaring yourself and a specific location no longer under your government's domain is "insurrection" exactly, but "secession" sounds close and is similar.
For something like insurrection, I think intention matters. I find it hard to believe the Jan 6 event participants were hopeful revolutionaries. I can't imagine even given the opportunity to have all their demands met that they'd undo any of the American government structure. They believed Trump really won the election and he should therefore be president. I don't think they were hoping to toss out the constitution, the congressional body, set up a king, etc. Comparing to the autonomous zones again, they explicitly desired such radical change. Those radical ideas were inherited from the less radical in action BLM events.
In terms of violence, deadliness, and property destruction, there's some BLM events similar to the Jan 6 event. There's also a few that were much worse and plenty that were rather uneventful.
In terms of National Guard involvement, there's again BLM events to both extremes to compare, except I would personally quibble with "calling out the guard" as meaning anything other than "not enough regular cops to manage it".
This final item might be tainted by my biases, but a major difference I perceive is reactions, especially in the media1. When comparing some of the worst of the BLM events we saw a general unwillingness of most media outlets and Democratic politicians to be critical, expressed in odd ways like insisting they were "mostly peaceful protests" instead of "a protest turned riot". The general lawlessness (especially in the autonomous zones) was largely ignored in Democratically controlled areas, and relatively much less in Republican controlled areas. With the Jan 6 event, nearly everyone (with few exceptions) is condemning it, calling it "riotous" and "lawlessness". There's little effort to try and cover the violence, understand their gripes, etc. Then there's the social media fallout. We can certainly argue it's different for Jan 6, but uneven treatment between the Jan 6 event and comparable BLM events is clearly evidenced here. And finally there's the eagerness by nearly everyone to find and charge the Jan 6 participants with photos of their faces publicly posted, while a judge ordered just the week before that law enforcement cannot use freely accessible images on social media to apprehend BLM event wrongdoers.
- Before Trump was elected I was quite skeptical the the alleged "liberal media bias". Maybe my skepticism was founded then, but at this point I'm very disheartened at the apparent bias in the media today.