My friend bought (second hand) a 300 2.8 for our Africa trip, with a view to probably selling it afterwads. She's been really impressed with what my 300 does and her 500 was just too big to take on a plane.
Now, a month later, she's decided to sell the 500! Not only was it too big for the plane, she's decided it's too big for her. The combined weight of the 500, Wimberly head and tripod (both of which were a neccessity) was just too much to carry around when going birding. The 300 is much easier to carry about all day and can be readily handheld.
I use my 300 with a Sigma 1.4x attached to it most of the time. I do own a 2x but I rarely use it (not sure why - must take it out a bit more often). If you're after wildlife in a forest environment then I'd suggest that, a lot of the time, it's going to be reasonably close so 420 mm may suffice. As for 'easily holdable', well there's no doubt in my mind that the 300 fits that description much better than does the 500.