Given the choice, would Tyson prefer to travel to the past or to the future?
It would depend on several factors for Tyson: how far in either direction that he could travel, how long he would be away for (in terms of staying in his destination and how much of an absence there would be from his leave), and whether or not he could return.
If Tyson would not be returned to his original point in the timeline, he would choose to go back in time by a handful of years. Far enough back that he can help smooth the passage of events whilst being near enough to have a clear memory of where help might be needed and that he can return to his own time without being too noticeably older.
If he would only be gone for a small amount of time, Tyson would favour the past where he at least has a vague knowledge to guide him, rather than trying to figure out an unknown future in a limited time frame.
However, if time spent away was as long as Tyson needed it to be and he knew that he could return back home afterwards, Tyson would choose to go to the future. Without a doubt.