ある and 有る are almost completely the same to native Japanese speakers.
Of course, 或る (a certain, some) is completely different, though. It's an adjective, not even a verb.
About thirty years ago, when there were no word processors, Japanese people almost always hand-wrote letters. At that time, more than 95% people chose ある, just because it was easy to hand-write.
Very educated writers, however, tended to use 有る. I think they just wanted to show their education level.
Today, in the word processor era, it's very easy to type kanji, no matter how difficult a kanji would be. Therefore, many people would choose 有る.
In many cases, writers even don't choose which. The word-processor decides which, and they just follow the automated conversion by the machine.
In case of the second sentence, you may wonder why ある and 有る are used.
Probably there is no intention for the writer who was a human.
The writer just followed the machine. lol
In my opinion, using too much kanji is too heavy, bossy, too-elegant.
So I personally like ある.
For example, はしを持つ is confusing. It can be 端を持つ or 箸を持つ, although 橋を持つ is less likely.
In this case, kanji is preferred in order to make the meaning clearer.
For example, せんせいにおうえんをたのんだがたぼうだからというりゆうできょひされた。
is difficult to read, while 先生に応援を頼んだが多忙だからという理由で拒否された。is much easier to read.
However, in case of 有る/ある, there is no difference. Both are two letters.
Therefore, I don't think the two have any difference.
Do you understand what I'm getting at?