No, there is no "more desirable". It's very much about personal preference. Find a horse with a personality, physical ability, and look that fits what you want and go with it.
AHA doesn't specify breeding "type" as far as Egyptian, Polish, Russian, Spanish, CMK, etc. Any good best will be able to tell you that about their horses, though. Some even go as far as to specify percent of each type. I.e. My horse is straight Egyptian and thre breeder has the breakdown of percentage of the major strains. I used to have it, but it's been lost.
From what I understand of Al Khamsa, it's more of an American organization. It's not necessarily a "type". Yes, all straight egyptians fall under al khamsa simply because they can all be traced back to the bedouin foundations, same for most if not all part egyptians. But, not all al khamsa are straight egyptian.
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