What's the difference? Big difference in recoil, range, and killing ability based on bullet weight and style and size.
The dealer want's to sell you a .243 that is on the shelf so naturely he's gonna tell you the .243 is better..... and if he's taling about the coyote hunting you've been mentioning, he's right. If you're wanting a "all around rifle" he's wrong.
It comes down to this, .. both rounds are great for many purposes... the 30/06 with more possible uses as far as taking larger game , ... the .243 better for the smaller end stuff .. both will put down coyotes AND deer with varying resluts as far as pelt damage and/or tissue damage. But the choice is yours .... BTW I believe you'll find that 30/06 (and 308 for that matter) ammo is generally cheaper when they run sales.
Even if you don't handload you can buy premium style .243 ammo with premium bullets for lots of special uses .. same for the 30/06.
I own one of each and love them both .. but there are things I'd much rather tackle with the .243 and the same goes for my 30/06.
Honestly .. if you're really looking for something that will help you better on both ends of the spectrum I'd go in the middle with a .260 or a 7mm/08.
But, the price on the .243 is ok ... I'd just like to see you get the accutrigger if you can afford it.
You might find a deal like DannyD's.