I do both. I hoop the quilt like some have said, stitch it out then sometimes fill in with FMQ. One teacher took us to a famous person's work in a book and said "look at her stitches" "she wins awards and her's are not perfect" "so get over it and enjoy it". That was freeing for me and I have been doing it myself every since.
What is fun on the Janome 11000 is to resize circles or stars and over lap some then quilt that all over a baby quilt.
I also use painters tape on the hoop grid so I know where the design will go. I seem to be able to move the hoop around and quilt quite a bit that way fitting them in.