Well my issue would be if I am going to spend the money for a mkii then why not get the 500 f/4?
Weight and size.
The 300mm f2.8 in any form is basically a "light" long high quality prime; able to take up to the 2*TC for a 600mm f5.6 lens. Yes if you can afford it and want the range and don't want 300mm then a 500mm f4 would be a better choice; its only downsides being:
1) It's heavier
2) It's bigger
2) It has a much longer minimum focusing distance - this is one lens where extension tubes are used for closer setups (eg when using a hide+feeding station approach - where subjects are coming closer than 5m or so).
Many a wildlife pro I know has the 300mm in the bag as a light option; or something similar, alongside the big heavies or just for days when they don't want the big heavy lens.
That said honestly its a question of finances and choice. If you have the option the best is to try before you buy - or considering the high price and the fact that most stores won't get them in to trial (unless they are a VERY Big store/national dealer), you can use rental. Rental has the bonus that you can actually get out and shoot with them. Of course its not cheap, but considering the high overall cost if you've no other option (no friends with one - no local club - no local store) then it might be a prudent choice to try each for a few days on rental and then make the final choice (for which you get first

)