I've had two ELCS privately, one at the Portland in 2012 and one at the Lindo in 2013. If I had another baby, I would try to go back to the Portland but with my Lindo consultant (we changed insurers after the first birth from Aviva to AXA and AXA wouldn't cover the Portland).
I only had private deliveries so can't comment on the consultants other than briefly - I had Pat O'Brien at the Portland and Raj Rai at the Lindo. Both are excellent surgeons, my scars are small and neat (Mr Rai's has the edge though). They both have a scientific approach to their job, not patronising, but more of a "this is how I like to do things and here is the medical evidence why" type. I wouldn't say that either was an old school smoothie or the mothering type, although both were very sympathetic to my pregnancy anxieties (I had a termination for abnormalities in my first pregnancy which meant I never subsequently relaxed). I did gel more with Mr Rai, whom you'll find described on various forums as 'quirky' but I'd happily recommend Mr O'Brien too. Mr Rai's secretary was much better to deal with than the Harley St Centre for Women.
In terms of the hospitals, I greatly preferred the Portland. I found the midwives more supportive, more forthcoming with pain relief and more helpful with breastfeeding. At the Lindo they were quite cursory when I asked them to help with the latch, positioning, etc. The nursery staff were a lot more helpful at the Portland. Food was much much better at the Portland while the Lindo was rather stodgy and boring. The Lindo also misplaced my NHS notes including my scan photos! Roomwise I would say there's very little between them, as the Lindo was refurbished in 2012; the only key difference I can think of is that at the Portland your OH has a fold out bed in your room while at the Lindo it's a reclining chair.
I would recommend touring them all, and checking out the consultants' websites to get a feel for someone who supports your approach to birth. As I was delivery only, I had no problems securing a consultant even at 24 weeks. Feel free to ask any Lindo or Portland specific questions.