My first child was induced by pessary. Took 3 of them and had an epidural and all the pain relief you could throw at me in advance of it, there was severe pain before the induction but I could grit and bear it. No screaming. Ended up with ventouse assisted delivery and episiotomy.
My second child was induced by balloon induction and one round of gel. They broke my waters and gave me hormone drip and the contractions ramped up so fast there was no time for pain relief. I begged for epidural! I ended up with uterine hyper stimulation, so baby came out in a flash. It was excruciating pain, honestly horrific, I screamed the building down.
The actual bit where the baby comes out... the actual pushing and the immediate afterwards part... despite feeling like I was dying, was completely better without the epidural. As other remarked, with epidural I couldn't tell I was having contractions, so couldn't push, and the Labour was so long the baby ended up in distress and got pulled out of me. Lots of drama. No skin on skin, baby went away to be treated medically. I needed a catheter and couldn't walk afterwards, longer recovery etc stayed in hospital for 5 days. Without epidural, I was able to push, which felt really awesome, my baby got put on me immediately after delivery, I was able to relax, have a bath, walk back to the ward, was home the same day.
In the moment, I would have absolutely taken an epidural the second time, as I said, I was begging for it, but it was physically too late. But retrospectively actually having felt the feeling of having given birth was so amazing that I'm glad I went through it.
Every birth and women different though... hopefully you are able to read everyone's experiences and decide on what will work best for you!