It is of course down to the shooter: I'd guess that for at least 90% of shooters, an Enfield-based target rifle will produce the same result as a modern target rifle.
I'm not a fanatical target shooter (as a military shooter I find it incredibly tedious that a target shooter can take 40 minutes to set up, adjust and fire just 12 shots....), but if I focus hard enough, I can usually place third or fourth, using an L39 or Envoy amongst twenty or so modern rifle users.
At short to medium ranges (up to 600 yards) I'd say an Enfield can still be competitive. For medium to long ranges (up to 1200 yards), you're starting to feel the disadvantage of a relatively short barrel designed for a slower round (the 144 gn NATO ball). When rebarrelled, Enfields do keep on going: One of the Envoys in my stock was the top-scoring rifle at 900x and 1000x during the 1994 Commonwealth Games. Its an Envoy fitted with a Madco stainless barrel and a target butt, but otherwise standard (top rifle in photo).
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