Help, Oh Wise Ones! I'm pulling my hair out! Lodging Question

You've done your homework (not everyone who posts questions here has)!
You're correct about London sights being spread out, so that what you said in your next to last paragraph is absolutely correct.

Our London experts are now abed in England, these are our regular contributors who live in the UK--look for their responses in the morning.

Based solely on location, the flat near Earl's Court is more conveniently located. Earl's Court is on both the Piccadilly and District Line. Parson's Green is on a branch of the District Line.

They both look nice but based on location I'd say the first one that is close to Earl's Court too. Kensington is a really nice area and that tube station will get you elsewhere quickly.

We stayed in the Earl's Court area last year: conveniently located to the Underground/Tube lines.
And easy to reach from Heathrow on the Underground, even with your baggage--a cheap ride into town.
It's not "in the center" but in London being "in the center" is not the advantage it is in some cities (say, smaller cities/towns), because of the large geographical area over which the London "sights" are spread.

You are correct in that the sights in London are spread out. Correct me if I am wrong, but I think if it takes you 20 or 25 minutes to reach somewhere, there isn't much difference overall. You can pick which flat you prefer internally and size-wise.

Both flats are located in areas where the better paid professionals live. The Earl's Court/Brompton flat is located slightly closer to the centre and on a quieter street. Earl's Court (EC) is Zone 1 for the tube but Parson's Green (PG) is Zone 2, making each trip slightly more expensive for the latter.

PG is nearer to the river if you wanted to have a walk down there and Putney is nearby, which will give you a different choice of where to eat. PG is on a better bus route than EC, as the buses from here will take you to Chelsea (great shops and people watching), Knightsbridge (Harrods), Green Park (the park and Buckingham Palace) and Piccadilly Circus (West End and theatres). Buses take longer, but you see more than travelling underground. Buses from EC just go the to museums, so you cannot get into the west end without changing. Both areas are as safe as you can be in London.

Buses have ticker tape signage saying which stop is next which makes it easier to work out when you need to get off. They are half the price of tubes too! There is also a night bus on the PG route if you were out after the tubes stop running at c midnight. Cabs will cost more from PG as it is further out. EC - the night buses do not run close to the property.

There are local shops close to both, with PG being the slightly more upmarket, but there is not much in it.

I probably haven't helped in your choice, but on the face of it, both seem as though they would suit you.

They are both nice, in nice areas, but if the money is right, closer in is better, therefore the Bolton Gardens property. If you can walk reasonable distances (a few miles), then loads of good stuff is walkable from there. London is big, but most of the main stuff is within an hours walk from each other.

Maybe split your days into 'areas', like Westminster, South Kensington (museums), Tower Bridge, Oxford Street, South Bank, etc. and walk around all the stuff that's in that area on that day... get to the areas using the tube. Walking is by far the best way to see London in my opinion. Wander about and get lost, relax and enjoy yourself, then hail a Black Cab back to an area you know when your done. Only likely to cost £10-12 or so. Make use of the Tube, it's super easy, and with an Oyster Card, has a maximum cost of £6.40 per day, if you stay in Zones 1-2, which is the main bit.

Travelling between Zone 1 and Zone 2 is the same price as between two Zone 1 stations these days except at peak times - and the same if using a daily/weekly product. There are 12 trains an hour from Parsons Green plus the 22 bus.

You probably already knew this: when you post a topic that starts with, "Oh Wise Ones...", you're going to get lots of replies.