There are 2 RCTs that address this question: 

• Both include patients with unilateral, isolated humeral shaft fractures.
• They both compare the same interventions:

            - Surgical repair with a bridge plate and screws

            - Functional bracing (bracing with hard plastic brace & adjustable velcro straps that can be tightened as swelling reduces post-injury)

• Both use the same scoring system to measure outcomes: the DASH score
• The Disability of Arm, Shoulder, and Hand is a validated scoring system that assesses level of disability after an upper extremity injury
• It is based on a patient responses to questions about functionality and is widely used in orthopedics studies

Matsunaga et. al.

RCT with 118 patients in trauma center in Brazil

Primary outcome: DASH score at 6 months

Results:

Student t test was used for analysis

Mean +/- SD:

16.9 +/- 18.0 for brace group

10.9 +/- 10.5 for surgery group

p = 0.046

Statistically significant difference. HOWEVER, the difference in scores is 6 points (16.9-10.9). The minimal clinically important difference (minimum DASH score accepted as representing a difference in functionality that is clinically relevant) is 10 points.
So, this statistically significant difference may not be clinically relevant.

The study also noted that in the bracing group, 23% of patients had a severe complication (nonunion, malunion, not tolerating brace) and required surgical intervention

Rämö et. al.

RCT with 82 patients in Finland

Primary outcome: DASH score at 12 months

Results:

Mixed-model repeated-measures analysis of variance was used for analysis

Mean (95% CI):

12.0 (7.7 - 16.4) for brace group

8.9 (4.2 - 13.6) for surgery group

Not statistically significant.

In this study, 25% of the bracing group had nonunion and required surgical intervention in the first year, and an additional 5% also required surgical intervention for other serious complications.

Conclusion:

Neither study showed a difference in DASH score that was clinically significant when comparing surgical repair and bracing after unilateral, closed humeral shaft fracture. However, between 20-30% of the patients who initially underwent management with bracing ultimately required surgical repair for healing of their fracture.

References

Matsunaga, FT, Tamaoki, MJS, Matsumoto, MH, et al. Minimally Invasive Osteosynthesis with a Bridge Plate Versus a Functional Brace for Humeral Shaft Fractures. The Journal of Bone and Joint Surgery. 2017(99) 7: 583-592. doi: 10.2106/JBJS.16.00628.

Rämö L, Sumrein BO, Lepola V, et al. Effect of Surgery vs Functional Bracing on Functional Outcome Among Patients With Closed Displaced Humeral Shaft Fractures: The FISH Randomized Clinical Trial. JAMA. 2020;323(18):1792–1801. doi:10.1001/jama.2020.3182.​