Both my pregnancies went overdue to 42 wks with no signs of labour- in hindsight I think I just naturally have longer pregnancies as I was very aware of conception dates etc.
DD1 was booked for induction at 41+6.
In the early hours of induction day, my waters naturally broke, so I felt more comfortable with the idea that DD1 had decided it was time to arrive. Began induction process at 8am with pessary/ walking round hospital/ no real monitoring. 2nd pessary at 12midday and another wait/ walking/ bouncing on ball. Neither pessaries did anything, so at 4pm they hooked up syntocinon (?) drip & attached bump band to continually monitor baby heartbeat (not a head clip). This was the only point I wasn't keen on as my movements were then limited to sitting/ kneeling on bed, rather than being free to pace the room. Contractions came thick & fast, had only gas & air (I have hugely low pain threshold so was surprised). Just as I reached the point of feeling I wouldn't be able to cope with the intensity, the head was crowning, and within a few minutes/ 3 or 4 huge pushes, she arrived 
Apparently needed a few stitches but I was too absorbed in DD1's face to notice or feel what the doctor was doing down there lol, and I never experienced any pain or feeling it was different in the weeks after.
Recovery was pretty instant- able to get up & walk/ clean myself up/ no afterpains/ breastfeeding was easy to establish/ I felt euphoric & only experienced a few days of very mild baby blues on poss days 5 & 6.
With DD2, I spent a good part of my pregnancy worrying that I would go into natural labour at home, when I really wanted a repeat of DD1s induced labour- short but intense/ controlled/ knowing biggers drugs were available if needed/ no coping with pain at home unsure if it was time to go in. So I was more than happy when DD2 appeared to be following the same overdue path and I was booked for induction at 41+6 again.
However, on the day, I was given a heartbeat bump band upon arrival to monitor while they sorted out the first pessary. The monitor showed baby was in distress, so my waters were manually broken, severe meconium was found. As no contractions/ dilation hadnt even started, the consultant advised emergency csection.
Csection itself was painless & sedate (although scary for us as so unexpected). The recovery on the other hand was awful- 24 hours of being stuck in bed before my legs were taken out of compression pumps/ first night of screaming baby but unable to sit myself up let alone get to baby/ 3 night hospital stay rather than getting home within 24 hours/ pain, frustration & unhappiness at being so clunky/slow moving for weeks after/ at least 3 weeks before I could purely bend or sit down without feeling pain/ didnt feel completely back to normal until baby was 5months (as opposed to 2 days with DD1 induction). Breastfeeding was far more difficult to establish- babies who have been through a vaginal birth have the natural mucus etc squeezed out through the process, but csection babies obviously don't so DD2 wasn't interested in feeding/ wasn't hungry as her tummy was full of it. It was too painful to feed in the traditional hold across my stomach, and my failsafe method of lying down & side-feeding was impossible with the pain/ worry of csection splitting. Hormone levels dropped so rapidly that 24 hours after the csection I was a hormonal emotional wreck, and this clouded the first 7-10 days of DD2s life.
Given the choice again, I would choose induction over elective csection- for the faster recovery time of being able to pick up baby and walk around almost instantly, the painful hours of labour rather than painful weeks & months of csection recovery, the easier breastfeeding start, the more gradual hormone decrease.
Obviously, your situation is more complicated if baby is still breech etc, but on the plain question of induction versus csection, I would recommend induction every time. However, your midwife and consultants are the professionals, and their recommendations will absolutely be what they think is in yours and baby's best interests.
Good luck with your labour and I hope everything goes well for you regardless of what choices you make.
At the end of it all, you will have a lovely squishy newborn to treasure, so just try to relax and take the whole experience with an open mind/ go with the flow as much as you can 

