Stainless will be somewhat easier to care for; no finish to scratch off, and resistant to corrosion. And, depending on the specific alloys used in each case, the production methods, and any coatings in the bore, the stainless might be marginally more durable and, so, last a bit longer. It will also have the advantage of being heavier. Heavier means less felt recoil, which means more comfortable shooting for longer and faster follow-ups, if that is important. (Of course, this can also be disadvantage if you spend more time carrying it than shooting it.)
As for fluting making it "stronger”, it depends on what you mean by "stronger". Properly designed and implemented fluting can make the barrel more rigid. But that doesn't mean it’s better. One could easily account for the rigidity of the fluting through different materials or changing the overall diameter of the non-fluted barrel.
Moreover, more rigid means it's less prone to bending under load, but how often do you plan on putting it in a situation where bending under load can be an issue? (I'm betting not very often...) And, depending on the specific situation (stress relieving in production, the particular cartridge and load in question, etc), more rigid could actually be bad for accuracy since it would change the barrel harmonics. (Granted, that's not likely to be a problem with a quality barrel from a good company, but I mention it to illustrate the no-such-thing-as-a-free-lunch, trade-off here.)
As for heat: All else equal, greater mass means it’s a better heatsink and, so, will heat up slower. Meanwhile, all else equal, greater surface area (from fluting) speeds cooling, so it will cool faster after firing. But, once again, the specific material in question, coatings, finishes, overall diameter (and, so, surface area) factor in here, so it's not just a matter of fluted versus non-fluted most of the time. And, for most people, are you really going to fire this type of rifle often enough, fast enough that heating it up is going to be a problem if you go with the (lighter) fluted barrel? Or, in the same vein, if you do manage to overheat it, how likely are you to be under time pressure that keeps you from being able to wait for the straight barrel to cool?
Basically, my point is that, for the vast majority of shooters, the choice is academic. The pros and cons of each are unlikely to make a bit of difference under the conditions that most people will subject it to. So, really, assuming both barrels are produced to comparable quality standards, production methods, and materials (and, so, should be capable of similar accuracy), and assuming you aren't concerned about weight (either for carrying convenience or shooting comfort), it basically comes down to cosmetics. So, which one do you like the looks of better?
EDIT: Between the two cartridges: Both are good. The .270 will be easier on the shoulder and wallet, is accurate, will be effective on most "non-dangerous" game animals (but check local laws for minimums in your area), and offers a pretty flat trajectory within its effective ranges. But, the .300 Mag will offer significantly longer maximum effective range, better performance against larger game, and, if you plan to load your own ammo, a much better selection of projectiles. Good luck!
