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I don't really have an understanding of this from corporations, but was wondering why a company would rather go being bought out for a lower share per price by a company that has less shares outstanding than for a share price which is a little more (like $2) but there is a a huge amount of stock outstanding?

So I'm not sure I'm fully understanding your question but...

Company A wants to be bought and has 100 shares outstanding. I'm the sole owner of company A

Company B wants to buy A @ $10 a rate of $10 per share and has 100 shares outstanding

Company C wants to buy A @ $12 a share but has 900 shares outstanding.

Assume that both companies are willing to pay out either in cash value for shares or will convert Company A shares to their companies shares.
Also assume that both companies are basically the same in terms of revenue and growth potential.

With company B I get to become a 50% owner, or just cash out my company to them for $1000

With company C I can either become a 10% owner or cash my company out for $1200.

Clearly if I want to windup my business and end my involvement Company C pays better, but if I just want to reduce my overall involvement but maintain an investment, it would be better to be a 50% owner in company B than a 10% owner in company

HTH