Its common, and yes a baby is still pretty easy compared to a 3 year old... and well, the older child is not so 'new' and 'cute' now after 3 years maybe... and the new baby is taking the show now.
But... if you really want to correct it... you have to change your mind-set. It is NOT just about spending one-on-one time with a child... because, children have extra "radars"... and they CAN tell, when a parent/adult is just "faking" or REALLY enjoying their time with them.
Next, if the older child continues to feel shafted and less 'liked'... then he may very well inherit behavioral problems. My sister did. She was the oldest. In fact, she "hated' me pretty much most of my life. Because she was jealous. She even told me that. Its miserable.
So be forewarned.
It wasn't that my parents 'liked' me better.... it was just that, i was the 'easier' child. And my oldest sibling, was never easy. It was just a personality thing too.
But, the thing is: it is all about changing your mind-set about it... you NEED to consciously make yourself, 'appreciate' your oldest again. Or... maybe you are just expecting TOO much from him, just because he is now the default eldest child. But a child, is a child. Not any better or worse, because of their birth-order.
It is like, when we are married an the lovey-dovey feelings comes and goes. We have to work at it. Right?
Only this is you dealing with a child now. So, really, it is not just about "doing things with" the child, but also displaying the feelings/attitudes toward that child too... for real. Genuinely. Because, the child will know if it is all just too forced.
A jilted child... is sad. And yes, your son as you said realizes how you feel.... he shows it in his actions. Be CAREFUL that his actions/behavior does not get more or acting out more. Because, the trigger for it, will be his feelings of being jilted or disregarded or just 2nd fiddle.
And all I know is, some kids are affected by it deeply.... others are not. BUT...it does form a child's childhood memories... or how it was when they were a kid. It can be corrected now... or for years and years and years from now... your eldest may STILL feel, that you 'favor' your youngest child.
When you feel like snipping at him verbally or getting cranky at him... you really have to stop. Or give yourself a time out. Walk away, take a deep breath... and APOLOGIZE to him. Kids NEED to hear their Mom/Dad apologize too.... and to feel validated. Otherwise, they will feel it is all just so unfair.
When I am in a bad mood and my voice gets snippy, I ALWAYS apologize to my kids. Always. It is NOT their fault.
You need to nip it in the bud. Your 3 year old, is getting real hurt by it. I am sure. I know, you are not a terrible Mom, you are just being honest. But think about your son.... they have just tender hearts. He will not be 3 forever. Change your mind-set.... and then the heart will follow.... and then the actions... proving to your son, that you do care and you have not changed just because of the baby. And that he is STILL important, to you.
And, do NOT "expect" so much from your eldest... he is ONLY 3 years old. Not 8. Eldest children already have so much 'pressure/stress' on them... because everyone just 'expects' them to act and be older... when they aren't. Keep things age-appropriate.
all the best,
Susan