Should I pronounce “er” as [ɚ] or [aɚ̯]?
The whole syllable 'er' and the retroflex syllables 'er' (as in 'ler', 'ger' ...) behave differently regard to this question.

For the whole syllable 'er', 'er2'(而), 'er3'(耳) and 'er4'(二) are in fact different. 'er4' is pronounced as 'ar4'. See this article. As when the difference came I do not know. I only begin to notice this when I started doing research in TTS (Text-to-Speech).

For retroflex syllables, I haven't noticed similar phenomena. Every syllable seems to be pronounced the same.

But as said in the wikipedia article, the mentioned shift happens in certain dialects/accents. I am not familiar the variation of sound in dialects.

I do not think the pronunciation difference can make one sounds younger or older, or more formal or mare casual.