IMHO I'd say the K31.
Here's my reasoning. Firstly, I've owned M44s, M38s, 91/30s all russian make (can't comment on the finns, but I dearly want an M39 or something similar), and I also own a K31.
I bought my 91/30 for $100 and it's a pretty darn accurate rifle, accurate enough to shoot canned tomatoes at 150 yards at least...
The K31 by comparison will hit anything. Absolutely anything at any distance. I can't actually say I'm exagerating either, but it will always be amazing, I just need to put in the hours to shoot up to its par.
This leads me to the next subject - value for money:
My mosin 91/30 is typical of their quality. A little worn and dented, bluing a little worn, but still very functional and hard wearing. It cost me $100, but seems they're closer to $175-$200 now. This gun will outlast me and continue to perform exactly as it always has.
My K31 I got a little while ago in pretty much as new condition. I have heard that they get stock damage, but mine isn't showing it. I got it for $300 with a crud load of goodies. This gun looks brand new, and from it's complexity, I'm betting a gun made like this for the civilian market would be more expensive than AR.
AMMO!
K31 ammo has been dead and gone for quite a while. Reloading is your safest bet.
7.62x54R was available a while ago as surplus, but is now unavailable. Every so often there's a rumour that the ammo boat is coming soon and we will soon be basking in the land of cheap surplus ammo, but so far I've seen it happen once. I would start reloading for the mosin too.
General fun:
I don't know what you're like, but I hate denting or decreasing the quality of my guns. That means that I can't make myself take my rosses, mausers or enfields out in the rain. Because of that, I shoot the mosin more than any of my guns. It was rough when I got it, and provided I don't beat it against a rock, my using it doesn't seem to wear the remaining finish much at all.
If you're looking for the best rifle to shoot with the utmost accuracy, buy the K31, it's one of the most undervalued rifles on the market that I've seen.
If you want to hammer around in the bush and blow the snot out of stumps and cans of tomato soup - the Mosin is your go to rifle.
In the end, save up, and buy them both.
P.S. - if you're in thick brush, buy an M38 or M44 - the 91/30 can be a PITA to move through deadfall.