Mbps download capabilities of my Mac Pro

I recently upgrade my Comcast ISP to 600 Mbps download. I have tested that with the app from Speedtest and my download speed as been averaging around 550 Mbps however when I test it using a browser other than Safari because it is outdated at the Speedtest website the average has been about 300 Mbps. So according to the two tests I am losing about 250 Mbps somewhere???? Comcast says it is because I am using an older device and OS but they couldn't explain why the app was getting 550 Mbps. Is this true and if it is, is there anything I can do (short of buying a new computer) on my Mac Pro. Please help.