We cut both on the router. For acrylic, the key is faster feeds and moderate speed. So we'll spin a 6mm two flute at 19,000 rpm and cut at 4000-6000mm/min (100um/tooth). As with all cutting you are aiming to take he heat out with the swarf so you have to move faster than it can.
For fibreglass/carbon, we use a diamond cut bur, spun as fast as we can and cut fairly slow, 60KRPM and 500-1000mm/min