Would I REALLY get much of a benefit from upgrading my scope?

1) Am cheap
2) Inherited Old Winchester Model 70 .243 bolt action (Labeled Sears Model 53) with cheap 4x Bushnell scope.
3) Have few hunting skills. Hunt behind Los Angeles in the Angeles National Forest. Ranger friend locates fool proof spot for me every year.
4) Normally shoot deer at under 50 yards. [...]