As someone who has a 6.5 Swede, I'd suggest something a bit bigger, particularly if you don't handload.
The Swede isn't all that more powerful than a .243, maybe 150-200ft/lbs, so I don't know you'll see a big difference with your .243. I suppose you'd get the option of heavier bullets, which may be a slight advantage on heavier targets.
If you don't handload, most of the available factory ammunition is loaded with the heavier end of bullets, 140-156gr. Much of this seems to be coupled with quite mild charges (I suspect this is to account for some of the 19th century rifles knocking about in this cartridge). My experience chronographing these factory loads is that they don't tend to do much more than about 2,450fps (about 1,900 ft/lbs). At those velocities the trajectory will be a bit of a pain as the range goes out. There are also only limited options in the Swede from most shops I've tried.
I'm sure there are exceptions to this if you look hard enough, so it's just my general feeling on it. An exception is Norma, as a local shop sells a number of their loadings and the variety of bullets and quoted velocities looks good but they are pricey (between £2 and £4 a shot).
When handloaded the Swede can be a different cartridge. I've put together loads achieving nearly 2,700fps with the 140gr and 2,900fps with 120gr without using max loads and I've heard about people bettering these figures (although they are probably running a bit 'hot').
Personally, I'm not sure you'd see much of a difference compared to the .243 unless you push things handloading. If I was in your position I'd probably opt for a .270, .308, .30-06, 7x57 or similar in order to get more of a difference between you little and large rifles.