It turns out that vitamin D₃ (cholecalciferol) has the edge.
In the U.S., vitamin D supplements are available over-the-counter as D₃ (cholecalciferol; usually in 400–5000 IU doses) and by prescription as vitamin D₂ (ergocalciferol; Drisdol and others; often prescribed at 50,000 IU doses).
In previous research, vitamin D₃ supplements raised blood levels of vitamin D more than vitamin D₂ did at equivalent doses. The blood test we use to measure vitamin D levels is the 25-hydroxyvitamin D blood level (25OHD)
Now two new studies, researchers reach the same conclusion.
In the first, a randomized trial, 64 older adults received daily D₂ or D₃ (1,600 IU) or monthly D₂ or D₃ (50,000 IU). Mean 25OHD levels were about 33 ng/mL at baseline. (NOTE: levels of 30-50 are considered sufficient by most experts).
At 1 year, mean 25OHD levels had increased by 9 ng/mL in both the daily and monthly D₃ groups (to 41 ng/mL); while mean levels increased only by 6 and 4 ng/mL (to 39 ng/mL and 37 ng/mL) in the daily and monthly D₂ groups, respectively.
So, the increase in vitamin D blood levels was greater with D₃ than with D₂, whether the vitamin D was taken daily or monthly.
However, in ALL cases, the 25OHD levels remained in the normal range!
In the second study, another randomized trial, 33 adults received 50,000 IU of vitamin D weekly, in either the D₂ or D₃ form; the average baseline 25OHD was about 28 ng/mL – in other words, these patients were vitamin D insufficient. Levels below 20 ng/mL indicate vitamin D deficiency.
After 12 weeks, increases in 25OHD levels were significantly greater with D₃ than with D₂ – as the increase from baseline was about 40 ng/mL with vitamin D₃ (to a total vitamin D blood level of 68 ng/mL) versus only 22 ng/mL with the vitamin D₂ (to a total vitamin D blood level of 50 ng/mL).
Note that in both cases, the 25OHD levels moved well into the normal range of 30—60 ng/mL.
In Journal Watch General Medicine, Allan S. Brett, MD, writes:

On average, oral supplemental vitamin D3 — the form made naturally after exposure to sunlight — raises 25OHD blood levels more than does vitamin D2.
The authors of the second study conclude, with good reason, that D3 is preferable for correcting vitamin D deficiency.
Note, however, that U.S. clinicians often give D2 by prescription to vitamin D–deficient patients: One reason might be the availability of high-dose D2 capsules that can be taken weekly or monthly; another might be a mistaken impression that prescription D2 is “stronger” than an equivalent dose of D3.

My interpretation of the data is a bit different. At lower doses (1000 – 2000 IU per day), I think the vitamin D₃ is definitely the way to go. However, at higher doses (50,000 IU weekly or monthly), the vitamin D₂ appears to be more than adequate—and it’s usually much less expensive.
So, here’s what I teach my residents and recommend to my patients:
If your vitamin D blood level (25OHD) is less than 30, you can choose either of the following:

• Take 2,000 IU per day, with the largest meal of the day, for 4-6 months, then recheck the blood level. This dose can be purchased over the counter without a prescription.
• Take 50,000 IU per week for 12 weeks (3 months), with the largest meal of the day, then recheck the blood level. This dose is available only in a prescription form.