D7000 and AF Fine Tune

I have a Nikon D90 and looking to upgrade, two of the possibilities are the D5200 or D7000.  The D5200 doesn't include the AF Fine Tune and I'm wondering how big a deal that is?  I have both the 16-85vr and the 700-300vr.  My main concern is with the 70-300.  I noticed that it's not all that sharp on the far end and I was wondering if the AF Fine Tune would help with that or is it just the way the lens is and AF Fine Tune wouldn't really help.

I was in Botswana last summer and when looking at my photos, most being at 300mm, I noticed that they weren't all that sharp.  Granted that there was movement going on in the jeep at times which made it harder.

Any advice would be appreciated!

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'Not all those who wander are lost.'
- J.R.R Tolkein