The problem with flapdiscs is due to their flexible nature they tend to thin out the surrounding area when taking welds down.
I tend to use a (worn) blue flap disc for the first pass if the welds are very high (if the pigeon needed extra squeezing!)...you can take welds down to 1mm-2mm if you are careful then switch to the power file...but if it's somewhere that won't be seen I generally leave the weld a smidge proud. Obviously if it's on a wheel arch then it needs to be flat with surroundings.
I do like the power file....more control....a lot less noise and to be honest I enjoy the process. I don't like using the grinder for fine work....just annoying to use I think.