It will take you approx. 1/2 day each way to and from FRA to Berlin, with both Train or Plane.
Trains travel from inner-city to inner-city and thus are quicker to access but take longer. If you consider the time it takes to travel to and from the airports and the time you have to be there early for check-in, the difference is not significantly.
If you have only one day to visit Berlin, consider taking an overnight (slow) train over the ICE (fast). The cabins are quiet comfortable with coffee delivered in the morning, you save the hotel costs and it's cheaper than the fast ICE (and at night the slow speed doesn't matter).
There is e.g. the City Night Line (CNL 1259) train for 91 Euros non-stop. If you book outside Germany, check for tourist discounts.
Some scenery will be missed along the route by night train but during my last trip I noticed a frequent site of wind turbines that (despite their great environmental purpose) put a damper onto my sight seeing experience.
Source(s):
I'm from Frankfurt and travelled several times to Berlin by both Train and Plane.