Unfortunately, I know of no formal studies testing all inputs to see which is the fastest.
However, I'll make my case for Cangjie, below, with evidence. (skip to "The Case for Cangjie's Speed" if you like)
Complications that would hamper an objective test of which is the fastest method:
- Many input methods you might like to include in your competition don't have many users, let alone users who are skilled enough to compete.
- Naturally, the input methods with more users will be more likely to have high-speed typists than input methods with few users.
- So, in order to have a fair competition, ideally you should have an equal number of equally trained competitors in each method...
Why Cangjie has, perhaps, an unfair advantage in this regard:
Cangjie is free, has been around since 1976, is ubiquitous (especially in Hong Kong and Taiwan), and has been so popular as to inspire many variants and spin off input methods such as qingsong and Simplified Cangjie... You can even use it for free online. For example: http://chinesecj.com/ime/cj5.php (version 5)
Boshiamy, by contrast, is proprietary, newer, and has less penetration into the market...
In terms of market share of the shape based input methods, Cangjie would be bigger than android and boshiamy would be smaller than blackberry's rim. (though it seems boshiamy is becoming more popular with time)
I'm honestly not sure about total market share or speed of other shape based input methods, but I can tell you about the Chinese language typists I know.
The majority of all the Taiwanese, Hong Kongers, and Chinese I've met used Pinyin, Zhuyin, or Cangjie.
Beyond that, I know maybe 4 or 5 wubihua users, 1 boshiamy user, and 1 four-corners input method user. I know thousands of Chinese language typists, so those other methods would represent less than 1 percent of the market if my experience was representative of the broader market.
The Case for Cangjie's Speed:
"Experienced Cangjie typists can reportedly attain a typing speed from 60 cpm to over 200 cpm." (from https://en.wikipedia.org/wiki/Cangjie_input_method)
Here's a 186 CPM example using Simplified Cangjie 速成: https://yewtu.be/watch?v=zHf6qNs3Qqg (many others in the competition are using full Cangjie)
Here's a 230 CPM example using full Cangjie 倉頡: https://yewtu.be/watch?v=mkzOLoV6fxg
Anecdotally, I've seen Cangjie win accuracy and speed tests competing against jyutping, wubihua, etc...(on youtube) (I can't find the video I was looking for, right now, but will add it if I come across it again) (Here's an example where cangjie won out for accuracy: https://yewtu.be/watch?v=ymk17B_N8rk.)
Additional IME Speed Comments:
I've seen some videos claiming 400-500 CPM voice inputs for phones...
https://www.kocpc.com.tw/archives/232363 also reports Array chinese input 行列輸入法 as having typists with greater than 200 CPM.
https://ithelp.ithome.com.tw/questions/10000851 reports a cangjie record of 220 CPM, boshiamy of 209 CPM, and Array 行列 of 215 CPM.
Some additional reasons to learn Cangjie
(Other than speed) (If you're interested)
Cangjie5 can directly (without requiring software conversion of traditional->simplified like boshiamy) input more than 70,000 characters. (including: simplified, traditional, ancient variants, Cantonese, Japanese, Chữ Nôm, etc.) To my knowledge, this is the most of any input method.
The Cangjie method helps you to remember characters' shapes. (through geometric decomposition) You'll find yourself visualizing the characters as you type.
I believe Cangjie is the most accurate input method. ( For examples, see: https://chinese.stackexchange.com/a/48570/28803)
Learning Cangjie visualization enables you to easily use Simplified Cangjie to type phrases very ergonomically and extremely fast.
jjomn oh egi <---Standard Cangjie
jnohei <-------Simplified Cangjie
a. Visualize "non-violence" and type nnvie (Standard Cangjie)
b. Visualize "non-violence" and type ne (Simplified Cangjie)
(Basically, the visualization process is the same.
You just type less.)
You can try them out at:
Simplified Cangjie: https://www.simpleinput.com/?lang=en
Cangjie 5: http://chinesecj.com/ime/cj5.php
Anyway, I hope some of that information is helpful.