A tree farm of that size in a temperate climate would only produce ~1.7GWh/y (net). You are overestimating the productive value of trees by a factor of ~15.
A 5MW wind turbine can produce a maximum of ~44GWh a year. Your assumed figure of 1GWh is only 2.3% of its rated capacity. No-one would bother financing/building a turbine on that site if they could only harness 2.3% of the maximum energy possible. The average load factor of on-shore wind turbines in Denmark over a 20-year period was ~21%, so based on those, you are underestimating the productive value of wind turbines by a factor of ~9.
So, having assumed that trees are 15x more productive than they are in the real-world, and having assumed that wind turbines are 9x less productive than they are in the real world, it is clear that your assumptions are wildly incorrect and thus so is your conclusion/suggestion that trees are (or may be) 25x more productive than wind turbines.
The question posed in the title itself is interesting — if a bit vague — so I'll refine the question a bit and present an answer to that based on some real-world numbers and more credible assumptions...
"Under what conditions are trees more productive than wind turbines?"
Deciduous temperate forests have a net primary productivity of ~0.0186 kWh/m²/day. That translates to ~0.775W/m². (Refer to postscript for source and explanation.)
If we use a forest as a guide, a 250,000m² tree farm could thus produce ~193,750W.
250,000m² is a circle 282m in radius.
Turbines need to be separated by 3-10x their sweep diameters for a variety of reasons (flow interference being the main one). Given that site details are unknown, let's use the average of 6.5x.
A 282m radius field could thus support a single turbine with a sweep diameter of (282*2/6.5=) 86m. Such a diameter sweeps an area of ~5800m².
The turbine power output equation — P = 0.5 × ρ × A × Cp × V³ × Ng × Nb — is then rearranged to calculate the wind-speed required to hit the power target.
Assuming 95% gearbox bearing efficiency, 80% generator efficiency, Betz Limit coefficient of performance (0.56), and sea-level air density, the average wind-speed required to generate 193,750W from a 5800m² sweep area is 5.1ms⁻¹ (~18kmh⁻¹). This is the best-case scenario.
Using a more realistic generator efficiency (65%) and coefficient of performance (0.35) means that an average wind-speed of 6.4ms⁻¹ (~23kmh⁻¹) is required.
So, in short, assuming your climate is temperate, and your site is 'average':
- Trees would be more productive on sites with average wind speed < 6.4ms⁻¹
- Wind turbines would be more productive on sites with average wind speed ≥ 6.4ms⁻¹
Note: A 6.4ms⁻¹ average wind-speed is quite windy and only occurs in a limited number of places:
PS: You can look up the Mean NPP of various ecosystems here. Convert from grams to Joules by multiplying by ~20,000 (for deciduous hardwoods). Then divide by 31,556,952 to convert J/yr to Watts. Example: Temperate Deciduous Forests have a NPP of 1200g/m²/yr. 1200 * 20000 / 31556952 = 0.76W/m². It's possible to get more accurate numbers if you know the mix of species and the latitude, or if you have access to journals behind paywalls, but for general use you can just use the Wikipedia numbers for a satisfactory approximation.