A 30-06 would never be called a waste of money, even when you own a 308. The short throw bolt action of the 308 will seem tidy compared to the 30-06. You'll really notice the difference when you first shoot a few round and cycle the bolt. Sub-caliber rounds using the parent case of the 308 (243, 260, 7mm-08) can be faster and flatter than the 308 but not necessarily more accurate. (The current rage in accuracy bullets lies in the 6.5 caliber.) The 308 is also sized up in the 338 and 358. Here's where the lack of powder room shows up and keeps these thumpers way below their magnum companions (in range, flatness, "power" and kick). The 30-06 has also spawned a slew of children based on its case, the 270 best known among them.
In the end, what do you want to do and what would you like from your rifle? My SOCOM 308 M1A has a very dissimilar character from my Kimber LPT bolt 308--even though they shoot the same round. Neither of these feel like my AR-10. I enjoy these for different reasons and take them along with different purposes in mind. I like the low cost of bulk 308 and the quality of match bullets. I would use my 308s for anything north of varmints to deer and small black bear. My 30-06 in a BAR has virtually no recoil but doesn't remind me at all of my older Savage bolt action that lets me know in a rather unkind manner that it choked out a 180 grain projectile. Neither 30-06 feels like a Garand in the same caliber not like my 308s.
If you currently have a Remington 700 in 308, don't get the same rifle in 30-06. Look for a bolt action with different stock geometry, a semi-auto classic like the Garand, a modern semi-auto like the BAR Safari, or a sporter. The differences in character will add to the difference in calibers to give you distinct experiences when you're shooting.
Finally, think about a caliber so different that it would have a completely different use and experience than either the 308 or the 30-06. If you can hunt predators or varmints, think about the 20-somethings like the 22-250, 25-06 or 223. (Whether bolt, semi-, or AR, the 223 is versatile and a varmint buster.) Or look at calibers that would take elk and dangerous game. Starting around the 35 Whelen and moving to the popular 300 Win. Mag. and higher, there are many interesting choices. Ever shot a 45-70 lever action (or 450)? You might really enjoy a powerful brush gun. But no gun purchase that's well considered need be a waste. Each can be as distinctive as your friends, liked for different reasons. You never know what new rifle may expand your expectations and widen your experiences!