Choosing health insurance in Israel for my yeshiva boys?

My twins are starting yeshiva in Israel in Elul iy"H. They are going to two different yeshivas. Each yeshiva sent information on health insurance companies. One suggests Egert & Cohen (ask for Meuhedet in the comment box); the other requires that the student enroll in A.I.M. (American Israel MediPlan).

Does anyone have experience with these organizations and plans?
Does anyone know what the difference between these plans are?
Should I enroll the boys in the same or two different plans?

Mostly I'm concerned about "pre-existing conditions." One son has asthma and though not on meds currently, requires Albuterol occasionally. I don't know what effect the climate change will have on his asthma but am concerned about how he will receive medical care if he needs it. I'm not sure if our American insurance will cover him in Israel. (Guess I have to find that out...!) How will he get prescription drugs?

Does anyone have experience with medical emergencies while kids are in yeshiva/sem?

(Am I worrying too much?) Rolling Eyes

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"Happiness is a choice." Who is fortunate? HaSameach b'chelko: He who is happy with his lot.