The difference in your first pair, with try, is addressed here.
Try to VERB means “attempt to accomplish the action of VERB”.
I tried to open the door = I attempted to cause the door to become open.
If the attempt succeeds, the action of VERB is accomplished: the door is open. If the attempt fails, the action is not accomplished: the door is still closed.
Try VERBing means “perform the action of VERB to find out if it will accomplish some other purpose”.
I wanted to clear the smoke from the room, so I tried opening the door = I opened the door in order to clear the smoke from the room.
The action of VERB is presumed to be accomplished. If the attempt succeeds, the purpose is accomplished: the smoke is cleared. if the attempt fails, the action is accomplished but the purpose is not: although the door is open, the smoke remains.
In both of these, the clause with VERB is the complement of TRY. This is not the case with STOP: STOP only takes gerund complements. However, it may take an infinitival adjunct describing the reason for stopping:
I stopped seeing him = I ceased to see him; I no longer saw him.
I stopped to see him = I stopped in order to see him; I ceased doing what I was doing or I made a stop in my trip so that I might see him.
The active voice is speech that places the subject first, followed by a verb, and a place/object. Therefore the correct form is subject -- verb -- object.
The passive voice is speech that places the object first, followed by a verb (tense and a gerund), and the subject. Therefore the correct form is object -- verb -- subject.
None of these sentences are in the passive voice, since I (the subject), always comes first in each of them.
Most of these can be converted from active voice to passive voice:
I saw a person repairing my car. The car was being repaired by someone.
I saw a person repair my car. The car was repaired by someone.
I saw a car being repaired. / I saw a car be repaired. A car was being repaired.
I watched a man solve the problem. The problem was solved by a man.
I watched a man solving the problem. The problem was being solved by a man.
I watched a problem being solved. / I watched a problem be solved. The problem was being solved.
Notice that none of these use I, mainly because I couldn't find a logical incorporation. I suppose you could say (and use as a guideline):
The car was being repaired by someone I was watching.
The problem was solved as I watched.
The sentences I saw a car repaired and I saw a problem solved don't make sense to me because the past participle is just by itself. I would include words to tie it together with everything else:
I saw a car that was repaired.
I saw a car that had been repaired.
I saw a problem that was solved.
I saw a problem that had been solved.
I also think that adding a comma, though strange, is acceptable:
I saw a car, repaired.
I saw a problem, solved.
Best Answer
Both are equally correct.
I'd say that the second one is slightly better, though, because looking is meant to contrast with speaking. By using the same form in both places—“grammatical parallelism”—you make the intended contrast clearer to the listener.
There is no rule for which verbs are followed by a gerund, which are followed by an infinitive, and which allow both. Even worse, a few verbs change their meaning depending on whether you follow them with a gerund or an infinitive. This question on ELU has a list.