While fountain pens are nicer to write with, they are also more demanding than ballpoints (humidity, temperature, paper quality, writing surface, blotting etc.). Hence, for reliably being able to take notes it might be a better idea to carry a space pen (pressurized ball point) instead of a fountain pen.

However, if you can control conditions and for example write comfortably at your desk, a nice fountain pen is preferable.

Because they work by capillary action, if you have the pen uncapped for too long, the trail of ink on the nib can dry enough that it gives you a hard start.

Recapping and uncapping can be distracting to others. There are some pens that have a click action like a regular pen but they are SPENDY.

Some of the paper quality issues can be mitigated by the ink choice and/or nib size.

Fountain pens work well when you've a flat surface that you're sitting above. They work much less well when, say, you're standing and trying to write on a notepad you're holding in your other hand.