The F-15EX carries up to 22 AAMs, more than double the load of the F-16V. So, buying and flying the F-15EX is like 2 F-16Vs
Not quite. While the F-15EX (or QA) can conceivably carry 22 AAMs that load out is for internet advertising, not actual conflict.
Firstly that load out would impact both range and speed of the aircraft significantly. If you asked any F-15 pilot across the world if he wanted either double his weapon load or double his fuel he would take the fuel in a heat beat. Tactically, it is very unlikely that a single airframe will be able to identify, track and launch against 22 targets, or even 11 targets should he launch two missiles against each. Both virtual and real exercises such as Red Flag demonstrate that jets don’t need to fly out with massive AAM loads to complete their missions, even in high threat scenarios. They run out of fuel long before they typically run out of munitions.
Second, tactically how much better would it be for Taiwan to have two jets in one area that a single jet with a larger payload? A single F-15EX is not going to have better situational awareness than two F-16Vs, nor is the single F-15 going to be able to provide mutual support, nor will it be able to split if necessary and use its AAMs to target adversaries that are moving in different directions.
The EX is new and may not be exportable. The QA is almost as good, can be upgraded to similar capacity, and should be more easily exportable.
And likely more than twice the cost to operate per hour than the F-16V while introducing a new type to the Taiwanese fleet.
Curious though. In term of air defense. would it be more cost effective to order more Patriots as any full scale conflict with China would assume that the airfield will be cratered at the early stages of the conflict?
Taiwan also has the TK-III which is considered close to as capable as the Patriot. RAND did an excellent study on Taiwanese Air defence options in 2016, including the trade off between a large fighter force and a large SAM force in the following study, https://www.rand.org/pubs/research_reports/RR1051.html
The report also considers the implications of Taiwan replacing its current fighter fleet with the F-35B, and utilise the reduced runway requirements and advanced stealth that airframe offers, to offset the loss of runways.
You can download the HTML for free and I suggest having a read to understand the pros, cons and costs involved.