I have owned a 700 VS in .308, a PSS in 308, and my father has a VSSF in 22-250. We are far from experts, but the reason we use these is to take for granted that it is US that needs to improve, NOT the rifle. I did make a few batches of 168 gr. BTHP that got me less than 1" over sandbags. The 22-250 has never put any bullet anywhere other than exactly where it was aimed, but we don't take full advantage of its potential, we only shoot it out to 300 yards or so. (Coyotes.)
Last month my father was handed off an older model medium weight 700 in '06, with a beat up Burris scope. We took it out with a box of 200s, and proceeded to put every one of them through 2". I can't think of anything I can't do with a 700. I just bought a rock chucker setup and the appropriate dies, this is the project for the summer, to REALLY learn what the hell we are doing. (I still consider myself very much an amateur.)
The Steyr might be fantastic, FN makes precision lines, you can get lots of rifles that might well be better than a stock Remington 700. A good friend of my dad's specializes in building custom rifles on Mauser actions that are the best I've ever shot. The question for myself, and MOST OTHER SHOOTERS I KNOW, is: "Are you really a good enough shot with the rifles you have to justify getting a better one?"
Sure, I would love a .308 set up in a AI stock with all the trimmings, but until I really nail the fundamentals for good, with all the knowledge of all the loads tested, it's a waste of money. I've sold $3,500 guitars to guys who really can't play at all. I was happy to get the commission, but it's a waste of money.