(Raw stats courtesy of NFLfastR. Original analysis by me. All OT games since change away from sudden death)

Pct team that gets the ball first wins: 53%

Pct both teams get the ball: 78%

Pct a team that scores an opening TD was favored to win: 69% (favored by an average of 5 pts)

Pct a favored team wins an OT game: 54%

Pct the kicking team wins if they stop an opening TD: 57.5%

Pct the kicking team can win with a FG on their first possession (incl games they dont get the chance): 60%

Conclusions:

Once a team that kicks off prevents the opening TD (which is very likely), they become favored to win and 60% of the time, they have an opportunity to win with a FG on their first posession.

When a team gets the ball first and scores a walk off TD, it's incommon and most often because they were the better team anyway, favored by nearly a TD on average.

If you are a team with an average or better defense, you are probably better off deferring in OT by the numbers. However, better to lose in OT having chosen to receive than to defer and be in that 22% that gave up a walk-off TD. Much easier to keep your job as a coach doing the thing everyone else does.