Why does cost of the travel from zone 1 to zone 3 in London depend on means of transportation?

Aw, that's one of my old commutes (although I lived in Southfields, so pretty much had to take the tube).

Without sitting in their pricing meetings, I'd suggest it's supply and demand.

As you said, the tube takes longer, but is cheaper. People are prepared to pay more for timeliness / shorter journeys.

In addition, there may be more people on one than the other, and people may be prepared to pay more for more comfort. Similarly, by raising prices you can spread load as people look for the cheaper options.

Finally, it may cost a lot more to run one than the other, depending on maintenance, fuel and service costs. To offset this and keep it running, they may be required to charge more for it.

So to add further confusion to the mix, I think it massively depends on the ATOC.

For GWR services, if you travel from a NR station say Drayton Green (Zone 4) to Paddington NR (Zone 1) the cost is £3.90 peak and £2.80 off-peak. However if you then interchange onto the tube at Paddington and continuing to somewhere inside zone 1 like Oxford Circus the price is exactly the same.

Doing the same on SWR services, from a NR station, say St. Margarets (Zone 4) to Waterloo NR (Zone 1) the cost is £4.10 peak & £3.00 off-peak, almost the same price. Interchanging onto the tube at Waterloo and continuing to Oxford Circus would mean the total journey price is £5.80 peak & £4.50 off-peak, around 50% for the same number of zones!

So much for travelling by zones being equal pricing, no wonder TfL got rid of the fare PDF chart from their website as all these nuances are now hidden!