I've owned a few 6.5x55's over the years. I currently own 2, but one of those was acquired recently, and just last night I mounted a scope on her. I'll be taking her to the range on Saturday to see what she can do.
Over the years I've owned about 10 different 30-06's. I currenlty own 3.
I only tell you this to let you know my familiarity with these cartridges.
I've taken more deer with the 6.5x55 than the 30-06. I think it's a great deer cartridge using 120 to 130 gr bullets. Of course bigger bullets also work well, but I like the velocity that these bullet weights allow.
The 125 gr Nosler partition is the perfect bullet in my opion for hunting deer with this cartridge.
When I hunt something larger like moose or elk, I prefer something a bit bigger. That's not to say that the ol' Swede round couldn't do it, but my preference is to get a bit more weighty bullet, like a 180 grainer, going faster than what the Swede can muster.
As a side note, let me tell you what I know about hunting in Sweden. My brother has been living in Sweden for the past 4 years, and has been out a couple times. First of all, only hunting clubs are given tags, not individual people. So group hunting is how it is done. In the summer these clubs go out to their designated hunting grounds and they clear shooting lanes. There are specific shooting stations and any one station is within view of the adjacent ones. The shooting lanes go between the stations. So when they hunt they use dogs and a couple dog handlers. The dogs go and flush the moose to run across the shooting lanes. The shot comes from one of the shooting stations as a running shot when the moose crosses the nicely cleared out lane. THe shots are normally 80 yards or thereabouts. Then, if the moose is only wounded, they use the dogs to track it down and finish it off. So in this circumstance the 6.5x55 with 160 gr bullets would be great.
This is just what I've got from my brother who has participated with a club. There may be some variation across the country, but from what it sounded like, not very much. This seems to be how all the moose huntng is done there.
But North American hunting is quite a bit different, and for the circumstances I find myself in when shooting bigger critters I like to have a bit more reach, but that's just me.
So, for a one rifle battery, given the two choices, I'd take a 30-06 over the 6.5.55, unless I was really only planning to hunt Mule Deer and smaller game. If I were just planning to hunt deer and coyotes, then the 6.5x55 would be my pick. But if an elk or moose hunt were likely then I'd pick up a 30-06. It really is more versatile. Especially if you're not a handloader. That's my preference based on the experiences I've had with both cartridges. YMMV.