Take a look at your portfolios ( money and pictures), if you tend to take a lot of slower speed or long distance photos then you probably would.
With IS the 300 F4 it is invaluable when I go indoors to shoot HS musicals and the orchestra. Outside with birds and jets not so much. I'll shoot jets in flight with a 1.4x and no IS. Hard but possible.
The other portfolio dictates 2.8 or 4 and the wife trumps all. For me it was going to be 70-200 F4IS or 300 F4IS and I needed the length more than zoom. I do not regret it and eventually I will get one of the versions of the 70-200 IS but a wide angle or body will come first.
The 70-200 F4 is very slightly sharper.
2000 740i-Annalisa and 2008 335i-Weebl. Weebl may wobble but has DTC