I had both at home with different teams.
DD1 - NHS homebirth. She was born with me flat on my back on the bed. I had a really short labour and they'd asked me to lay down for a VE to see if i was in active labour yet and her head was actually crowned already. I pushed her out and she was put onto my chest and the mw immediately clamped the cord and asked did XP want to cut it. He said "but we'd wanted to wait" and i said "it's clamped now, you might as well cut it". He did so. DD, whose first apgar was 9, went blue. They lifted her off me and took her to the window to see her colour better. They suctioned her nose and mouth and then brought her back, put her on my chest and put the oxygen tube flowing under her nose. She pinked up and cried a little then.
The mw began to pull on the cord. I didn't like it and felt worried. She seemed very concerned. She asked could she give me syntometrine. I assumed i must be taking a long time or bleeding too much so i consented. She gave me the injection in my thigh and i remarked on how much it stung. Later i read in my notes that the 3rd stage was 12minutes total and i bled 250mls (NOT a lot)!
After about 40mins DD was hungry and had her first feed. The mw sat beside me supervising her latch and giving tips. After that i got up and had a shower, and managed to pee. Then someone made me toast and we all had cake and tea and toasted the baby with our mugs. After 2 hours (from the placenta coming) they did a set of obs, felt my uterus (which was at my navel by then) and left. In the UK in those days a MW came every day for 10 days then a health visitor came every week (2 visits in total) then you went to your appointments in clinic.
DD2 - independent mw homebirth. She was born with me on all fours leaning over the bed. As i was pushing her out into my hands my MW was calling to me "you're doing it all yourself! You're doing everything!" with a huge smile and congratulatory tone. In fact i had to let go of her to get her shoulders out as it took so much effort (she didn't turn to deliver them) and the MW and my hands touched as she passed her forwards to me. She began to scream as her chest was sliding out of me and was salmon pink when i got her against my chest. I sort of half-twisted round to sit on my bum and hold her against me, my speedy mw had already thrown a pre-warmed towel over her in my arms. I shuffled her about so i could see her, and as i did so i felt between her legs, then once she was more on her side/back had a look to confirm that she was a girl. The mw then said "you know she has a true knot in her cord?!" and we all looked at it and discussed it and it's relevance. The knot had been loose when she came out but was pulled tight by her being held against my belly/chest. She was very pink and screaming and obviously not at all suffering from it! I smiled broadly at DP and said (no lie!) "That was fun, let's do it again!" and everyone there (MW, student MW, my dad, DP) laughed and laughed and the mw said "what NOW?" and i replied "well, maybe i'll get this placenta out first" and we all laughed again. Meanwhile DD screamed on and off. The mw asked did i want to try to have the plcenta and talked to the student (who had never seen a HB) through it, telling me at the same time "tell me when you feel a pain and a gush". When i did i told her and she had me kneel over a little dish and the placenta flopped out and then she showed it to us all with it's strangeness (it was heart-shaped, with a marginal and velamentous insertion and of course the knot). Once it was out we had cut the cord and i continued my efforts to get DD nursing (she was utterly disinterested and only wanted to cry until we cut the knot off). She nursed great for about ten minutes then fell asleep. I cuddled her, switched her to the other breast and in doing so woke her and she nursed again. The mw and student went downstairs with my dad and left DP, DD and i to bond. After about 15mins my dad joined us and it was just lovely - i was still sitting on the floor on a towel-over-showercurtain-over-duvet so was very comfy and i just snuggled and nursed the baby. The MW and student came back a time or two to do obs (my BP, pulse and temp, baby's pulse and temp). After about an hour the MW asked did i want to have a bath run for me and i said i'd prefer a shower and asked DP would he come too. So DP took the baby and i waddled to the bathroom with a chux between my legs to catch drips and i got in the shower while DP sat on the loo (with the lid down) with a sleeping DD wrapped in a fresh warm towel in his arms. I washed my hair and body, gently hosed off my hard-working vulva and my midwife came in and out ostensibly tidying up but in reality checking i was looking ok. I was brought fresh underwear and gigantic pads and slipped them on as i dried off. Meanwhile my dad was downstairs grilling 3 packs of bacon and when i got back to my (freshly made) bed there was a hot cup of tea and a bacon sandwich on its way up the stairs for me. While we ate my dad snuggled the baby, then the MW checked me for tears (nothing needed stitching) and looked over the baby for obvious issues (not the newborn exam, our GP came and did that on day 4) like talipes or imperforate anus, and found nothing of note, then the mw and student left. My MW would normally come back the same day (if the baby is born before noon) but when she phoned to see if we wanted her we were all asleep and she let us continue to sleep. She came every day thereafter for 10 days, then twice a week until the 4th week whereupon she stopped being my mw and became a very good friend (i still see her every week!).