Can't go wrong with either one. When I was thinking about buying my first rifle ( circa 1969) , I was considering 270 vs 3006.
I went with .270 and never regretted it. If I were starting over , I would look closely at 7/08 in a short action or 280 rem in a long action.

A little more flexibility in bullet weights in 7mm .

MO

have both...seem to gravitate to the 308.

Yep flatter shooting more energy winner winner chicken dinner.

Unless, you like----------the .243

.270 is my preference. Been deer/hog hunting with it for 8 years.

Can't go wrong with .30 cal. After the last episode of ammo hysteria the Country threw itself into, NATO calibers (7.62 x 51, .45acp, etc.) were about the only thing available with any semblance of regularity...at least in my area. 7.62 x 51 (.308) was chosen as a standardized caliber/round so it could be shared with and also produced by NATO allies. So, there's a bunch of it out there...worldwide. Not sure that stupid ammo hysteria will ever hit us again but something to consider, IMO.

You mention pigs, deer and budget. Not enough of a difference between the two to say one is better than the other based on those three qualifiers, IMO. Gun price will probably be slightly lower with a .308, although Academy has a deal on a Rem M783 .270 for $299.99 right now. The 783 in .308 is $349.99. Ammo price will be slightly cheaper in .308 but who knows what it will "like" to shoot? Brother and I purchased exact same Model 700s in .308. Mine shoots the Remington CoreLokt (cheaper end of the ammo spectrum) like a dream. His, not so much. Think he finally found that some "match grade" ammo, Federal maybe, groups best in his and it is ~$20/box more than the CoreLokt. Either gun, properly dialed in, will make anything walking around in Texas DRT (dead right there). Unless you expect to be regularly targeting things outside of 300 yards, I wouldn't burn a whole bunch of energy trying to figure out which of the two will best suit your needs.

Find a deal on the gun and spend your money on glass.

I'd do a 7mm magnum. Can shoot a variety of loads.

I LOVE my Remington 700 in 25-06. Might want to at least look into that caliber.

JR

308 is my prefence of the two, you can't go wrong with either.

I love my .270 and remember the .270 is a 6.8 mm so it was the 6 mm before the 6 mm rage

.270 gets my vote. Has never left me desiring more or something different.

I've got a Ruger M77 in 25-06 that is my preferred gun. I love the round as well. They run hot and tend to burn out a barrel quicker than most other rounds but not an issue for most folks. 117gr @ 3200+fps...giggity!

The .270 does that with 130gr. rounds. I have a friend that grew up on a 30.06 and transitioned to the .25.06 and loves it too. Weve hunted together 50 years.

I've heard the 7mm mag is falling out of favor with shooters due to these short magnums. I like the 7mm mag and used my M77 to take my deer on opening day.

Both will outshoot the average shooter.

OP be sure to get a good scope.

The same thing is happening to the old belted magnums as it did to the .30-06 when the .308 came along.
Many people that don't feel the need the extra range opt. for the slightly reduced version.

You give up the heavier bullets in the caliber and a little bit of top muzzle velocity, but get a shorter, lighter rifle with a tad less recoil.