Is there a big differance between a regular rifle barrel or a heavy/bull barrel in .223, .243, 22-250?
looking for a good long range coyote rifle (200+ yards)but on a budget and most heavy barrels in those calibers are quite expensive

remington sps varmit 530 bucks

thanks i'll look into that. but is there a real advantage of the heavy barrel of the standard rifle barrel?

A heavy (varmint) barrel will tend to be a little more rigid, and take a little longer to heat up. They weigh more than a sporter weight, and tend to be more steady on a rest. They tend to dampen harmonics better than a lighter weight barrel also. Do they shoot that much better in the sizes issued by the major manufacturers than a standard weight barrel? Probably not a great deal of difference in most cases. There are lots of skinny, whippy-tubes out there that shoot just as well.
If you like the looks of it, and feel it may help improve your shooting, then go for it. I just really don't feel that a heavy barreled varmint rig is going to guarantee you get what you thought it would. Also, don't forget the added weight you will have to lug around unless you park yourself at the edge of a field when you go out. Just my opinion..........

In a hunting environment, I'll have to say NO for the yardages you mention.

Example: I have a Rem 700 Mtn. rifle (.270) and plink turkeys off @ 325 yards.

Maybe as a tactical rifle it might, but out to 300-400 yards I would have to say practice and a proper shooting load form your rifle is all you'll need!

Just look around and you can find some superb shooting gun for great prices.......heck our Gander Mt here in York, PA has a Savage 12 Varmint bolt action in 223 with the heavy 26" barrel looks like brand new on the used gun rack today for $379.
Not a "pretty" gun but with that Accutrigger it can shoot lights out as far as you care to try.