If you do a search on either calibers you will find many happy 30cal owners here, me as one of them.
Personally, with a 30cal and in a short lenght barrel, I would opt for the 308 in a 22" barrel as it doesn't give as much up, and takes less powder to reach velocities that a 30-06 does up to a certain point grain of bullet. Still the history and versitility of a 30-06 is a very nice point. Both are great cartridges.
Kinda depends on you hunting enviorment too. If you need to take long shots of in your in closer areas. The 30-30 has harvested deer and then some. And for a Single Shot Handi, your reloading possibilites are very versitile using all spitzer type bullets.
Then there is the 270, 280 with a 26" tube
, and many other choices like the 35 Whelen and 45-70.
Depends a lot on what you looking at and what enviorment. Not to mention if you handload or not. It opens up SOOO many options.
-Aaron