Learn English – the path of vs the path to

I fear your categorization is based on unsound foundations, but let's just look at along:

The signs were on buildings along Main Street.

Passive.

He traveled along roads that were long and painted purple.

Active.

Assuming that I correctly understand how you're categorizing prepositions, then it's a preposition that can be in either state.

On the forum you linked to, a long catalog of uses was posted at 20-Mar-2008, 08:27. I think that posting makes clear that

1. there is no difference between the two phrases in the senses of "continuing to support/accompany/practise/adhere [figuratively] to": stick to/with the plan, stick to/with me, stick to/with your principles

ANOTHER EDIT: You may find one preposition used more often with any particular object stuck to—see bib's response—but this doesn't exclude using the other.

1. only stick to may be used to signify "cause to adhere to": stick the poster to the wall but not stick the poster with the wall.

2. only stick with may be used to signify "impose a (relative) burden upon": he stuck me with the bill or she got the fellowship, I was stuck with an assistantship, but to won't work in these.

One more "stick to" idiom occurs to me: *stick it to [someone]", meaning "inflict excessive (physical, emotional, financial &c) pain upon": They had him cornered and really stuck it to him.

EDIT: And another: Stick to [one's] guns, although it fits use 1 above, is a fixed idiom; stick with your guns would mean "continue to accompany your artillery".