I did part 61 for my CFI, but I don't think that 141 is that much different. I don't think it matters which one you do first. I thought that doing the CFI first would be a lot easier than doing the MEI. It was a lot cheaper for me to do my CFI because I was already proficient in the airplane I was using. If you are CFI and you go to a flight school that will pay for your MEI that a big bonus. But in the end it doesn't really matter.