Does anyone have a preference between these two powders for 180gr roundnose bullets? Looks like 4350 may have better loading density. What about with 220gr roundnose bullets?

Either will work. 3031, being faster, will require a lighter charge and won't get as high velocity given the same pressure. 4350 will take more powder but can generate a bit more velocity.

If you're not into high velocity, you can save a bit of money with the faster powder. Load density doesn't have a significant effect on accuracy in an iron-sighted battle rifle. Let the guys with heavy-barrel scoped cannons worry about that.

Maximum load data from an IMR booklet -

.30-40 KRAG
WIN. CASE; WIN. 8 1/2-120 PR
REM. 180 GR. SPCL
.308" DIA.; 25.5" BBL.; 3.00" C.O.L.
Powder  Grs. M.Vel C.U.P.
IMR 3031 38.0 2375 39300
IMR 4350 46.0 2445 38700 [compressed]

With the heavier 220 gr RN, IMR-4350 is your best bet.  40.0 grains under that 220 gr is about as close as you can get to the original .30 Army round.

As for the lighter bullets like the 180 gr, you might consider a slightly faster burn rate like IMR-4064 or 4895.  IMR 3031 is faster still, and although you could work up loads, I think it would be better suited for much lighter bullets like 150 gr and lighter.

Para... you beat me to the punch... and as usual, with much more detailed and specific info! 

3031 was a pretty good match for 30/30 130 grain flat points. I chose a load half way between minimum and maximum and was happy with the velocity and recoil. The flat tip bullets expanded pretty good at the higher 30/40 velocity. It would have been good for southern white tail and coyotes. A little light for pigs, some of them ran a pretty fair distance.
For 180 grain and up go with the forum wisdom and experience.

I was leaning towards 4350; although, I have had good luck with 3031 in the 7.65x53 previously so I was wondering. I have an old box of Winchester 220gr PowerPoints (wish I could still get those!) so duplication of the original army load sounds like something I need to try. Interesting story about the 220 grainers. Many years ago, my dad convinced himself that the 180 grain PowerPoints in his 30-06 were just not quite enough bullet for Texas whitetails. He bought the 220 grain bullets and had me load up some. I think he shot about 5 out of his 20” barrel 30-06 rifle and then he was done! I pulled the rest of the bullets so I have almost a full box. Thanks.

Funny my dad went  with  100 gr plinkers with 20 grains of Unique in 30.06. South Texas white tails are not that big!

Actually South Texas white tails had a reputation for being larger than hill country white tails. The state game biologists have made so many counter productive rules we are now having an over population of inferior deer. Every one in the local volunteer fire dept has quit hunting deer also, too many rules. I saw 20 deer in the 200 yards from the house to the shop, no big ones.
The only ones that get to really manage the deer herds are those with high fenced places that can hire private biologist to give them the go ahead to thin and cull. If you ask me the state biologist are making work for them selves, so they can manage private herds while wrecking everyone else's hunting.
Do not ask me how I really feel!

Texas deer hunting is not what it was not that many years ago. There are so many rules as you say. Does that buck have 12-7/8 inch inside spread or 13 inch? And to find a really huge buck you are going to have to pay the big bucks. Someone to drive you around and tell you which one you can shoot for the price you paid. And who has the nerve to hunt public lands???

"Load density doesn't have a significant effect on accuracy in an iron-sighted battle rifle."

So far in my jacketed bullet experiments, it appears to me that I get better accuracy with powders that give full pressure at slightly less than 40 grs.  Like the max 3031 load with the 180gr bullet that parashooter has posted.  That's been with bullets ranging in weight from 123gr up to 168gr.  Could be a lot of different factors, it's just something I've noted.