While I normally kill all of the enemies in my way during Vanguard strikes, if I have played the same strike two or three times in a row (which has happened quite a lot) I'll just skip as many enemies as possible to get it over faster. To my knowledge, yes, farming patrols will get you more rep than doing strikes. Marks from public events, on the other hand, is a different story. Some public events are more likely to happen than others and in different areas ("event A" in "Area A" may happen 90% of the time while "event A" in "Area B" may only happen 10% of the time) and even then, they only happen about twice an hour, while most Vanguard strikes can be beaten in 10-20 minutes.