I have owned (logically) both. I traded my 2000 Lincoln LS V8 in for my new 2006 Dodge Charger R/T, which is mechanically identical to a 300C.
The 300 is much larger inside (and outside) than the Lincoln, and has a much bigger trunk.
The 300C is much faster than the V8 LS. In fact, if you get a 300 with the 3.5L V6 and 5-speed transmission (the one with autostick) it will be about equivalent to a '00-'02 LS V8. All Chrysler 300s are faster than a V6 LS, except maybe the 2.7L base model. However, the 300 with the 2.7L comes with a 3.90 rear end which makes the car feel very quick around town. On the highway, you'll find yourself downshifting a lot.
Because the 300C is a bigger car with a much longer wheelbase, it has a much better highway ride. It does have a hint of big American car float that the LS does not have. The LS is more nailed down on the freeway and does a great job of absorbing bumps, but isn't as smooth. Around town, the 300C will accentuate bumps more because of its 18" wheels, with the LS arguably providing a superior ride. The Charger has a tighter suspension than the 300 and eliminates the highway floatiness.
The LS sits lower to the ground and has a more European feel to it. The 300 feels like you're driving a big American car. LS is definately the American BMW 5-series. The 300 is pure American muscle; the banker's hot rod.
The 300C offers almost all the luxury features the LS has except a few. Newer LSes can be had with cooled seats, which are not available on the 300. The 300 also does not have speed sensitive volume on the radio or a heated windshield wiper park (I don't think). Conversely, the 300C can be had with headlight washers, which I don't think you can get on an LS. Ultimately, the LS probably has more luxury features than are available in a 300C. The Dodge has far fewer.
The LS V8 has a great engine that always seems to have enough power on tap. The V8 in a 300C goes miles beyond that. Sure, the 300C has a couple hundred pounds' weight penalty, but with 390 lb/ft of torque it's just a completely different driving experience. My '00 LS was plenty fast, and the '03+ are even faster but the 300C blows them all away. The Dodge is slightly faster yet. The transmissions in both cars are great as well, but the LS has a reputation for some quirky behavior. My car never exhibited this, though. Ironically, I get better gas mileage in my Charger than I got in my LS. In my commuting cycle, I got about 18 in the LS, I get about 19.5 in the Charger with the Hemi.
Both cars are very comfortable on long trips, but the 300C extends this into the rear seat as well. The LS back seat is comfy, but just not very large and is tough to get in and out of. Both cars are also very safe.
I would definately recommend the 300C. It's bigger, faster, looks better (subjective), and much more economical to operate (better mileage, cheaper maintenance, mid-grade gas instead of premium). Every time my LS broke it was megabucks to fix. Pinion bearings, $626. Power steering pump, $615. And so on. My LS was also horribly unreliable - in fact, it was the worst car I ever owned. I bought it used with 40k and traded it with about 75k miles. I've put 14k on the Charger and nothing has broken yet, but of course it's too early to tell. Since the 300/Magnum/Charger are mechanically identical and being produced in huge quantities, parts should be plentiful and cheap, and the mechanic you ultimately take it to will have worked on one before. That will not be the case with the LS.
Take everything I say with a grain of salt, and go drive both cars. See how they feel and how they fit your lifestyle and see which one you like best. Whatever you decide, best of luck to you!