The Mk2 is a better and lighter lens that focuses faster with extenders. However the Mk1 is still a fine lens by any standards.
Whether the difference in quality and weight is worth the extra is your decision!
I had a similar dilemma back in 2013 and couldn't justify the cost increase to go to the 600 Mk2. However I found a reasonably priced Canon 800 F5.6 L IS. Sharper and lighter than the 600 Mk1 and less need for extenders too. It is heavier than the 600 Mk2 so it sits roughly in the middle for weight. It is also an F5.6 but this really doesn't matter to me as it is sharp wide open and I rarely (if ever) shot my 600 wide open.
If money is no problem then the Canon 600 Mk2 is the best choice in my opinion, but a second hand Canon 800 F5.6 L IS is a significant upgrade compared to the 600 Mk1 and cheaper than the 600 Mk2. It is all down to your personal needs and uses but the 800 works extremely well for me - might do for you?
Life is for living, cameras are to capture it (one day I will learn how!).