105 vs sora

Somebody really good, but I can't remember who, once said they had never won a race on Dura-Ace they would have lost on Ultegra or lost one on Ultegra they would have won on Dura-Ace.

New 105 5800 is superb. I have tried dura ace 9000 and could not say difference.
I have seen recently on merlin cycles full group for 253.

I have done this exact upgrade, I'd say that there is definitely a difference and the shifting is lighter, smoother and more exact.
Everything g in 105 just feels better quality than sora too and the hoods are confier (imo).
Also it needs less continual adjustment to keep the gears working perfectly but this was never much of an issue really.
There is probably about a 500g difference in weight too which I thought Did make a slight difference to how the bike rode.
Whether those changes are worth the money for you I cannot say, I only changed because I smashed up one of the old shifters and it was my birthday

Only if you have sensitive thumbs. I made the same upgrade (5703) - in part because I wanted to put a bar bag back on after some cable chafing issues and I preferred the cleaner lines - but all things considered I'd struggle to justify the expense, really.

In terms of shifting performance if you maintain both in good condition they will shift when you want it to, but a 11 speed groupset would offer you closer gear ratio on your cassette.