A No.4 (particularly a Savage or Long Branch) is allegedly a better, more accurate platform - many of them were converted to handle 7.62 NATO, which the SMLE can't handle, so the action is certainly stronger. Among other things, the iron sights (if you choose to retain them) are apertures on the rear receiver bridge rather than a rear V just in front of the chamber, which gives you a longer sight radius and better accuracy.
But the SMLE is excellent as a tough-as-nails, abuse-resistant platform to go hunting with if your ranges are short (around 200-300yd depending on the game you're hunting) and among the military bolt rifles it's got one of the largest magazines (where legalities don't interfere - they occasionally do) and fastest bolt actions on the planet. This is a firearm which is
literally legendary for its rate of fire and toughness.
The P14, if you can find one, is probably more like what you're looking for and it has a five-round box and a Mauser bolt. The .303 version isn't anywhere near as common as the SMLE and the No.4, and if I ever found one I would not dare to offend the Gods by sporterizing it
. Many of them got converted to other calibres because it was originally designed around a military cartridge that would give the 7mm Remington Magnum a run for its money (0.287" 165gn Spitzer at 2785fps) and it could run breech pressures that would send an SMLE to the smelter.
Sadly, Ruger discontinued the No.1 in .303 some time ago and they told me (when I asked) that they had no plans to reintroduce it.