I, too, usually split up stays in London, just to get credit and also to get the nice feel of different neighborhoods. That being said, I've spent the last three years minimizing use of the ultra-simple, yet irritatingly expensive and somewhat unreliably fast Heathrow Express. Quite simply, the tube was ALWAYS my choice when travelling light (one rolling case, usually a carryon), just because it was scads cheaper. Yes, it takes an additional 20 minutes; so what? Especially early, it's uncrowded headed toward LHR, and that leaves us with an additional GBP 20 to have spent on dinner!....

That said, I *like* the Paddington (if the price is right) since they reliably upgrade me, there's decent tube service you can access essentially indoors, and the breakfast has always been good (and included for these Diamonds). Bus service is frequent and while we don't spend a lot of time in the neighborhood, it's not far from where we seem inclined to go. Probably every other trip to London, we stay there on one end or the other (but not both).

We hardly ever stay at the London Hilton, since it's almost always a LOT more (and I can't justify it). I prefer the (sorry gang) Park Lane (SPG) in Mayfair, or the Trafalgar or Waldorf, or (RIP) The Langham. The new Hilton property off Regent Street is on the list to try, but I'm afraid I fell for the current 52-quid specials at the Kensington and Olympia for the next trip, so perhaps later this year I'll get my review in on that.....

The only properties we avoid are the Hyde Park (tired) and the Green Park (no Diamond recognition, no a/c, no breakfast---and sweltering in summer).

In the OP's situation, I'd size up the London Hilton's premium. If (1 night London Hilton+tube to LHR < Paddington+HEX+cab fare), the choice is clear--LONDON HILTON, and use the bus or tube, but skip the HEX. But otherwise, if you haven't tried the Paddington, you might save a bunch, see a new neighborhood, and slip seamlessly to LHR on HEX. Might even try 2 nights at Paddington (my choice, usually, and then hold my nose for the HEX fare, or STILL use the tube if I'm travelling light and by myself).