To sumarize:
Sheraton Heathrow:
- No Club lounge (though maybe one coming someday)
- Off the "free ride zone" and thus makes it inconvenient to get around. Cheapest way to Hatton Cross is 1GBP bus ride on Bus 81 with change to one of several busses on to Hatton Crossbefore you get to Harlingen Corner
- Irons and Ironing boards from the Victorian era
- Often cheaper than Sheraton Skyline

Sheraton Skyline
- Club/Lounge as described in the thread
- On the Free ride bus zone between T1 and T4. Good free access to Hatton Cross tube line via several busses
- Just a short walk from The Pheasant.. a nice pub with pretty decent food

For me, Skyline is much preferable, though as an SPG Gold, I don't get diddly from either as far as upgrades, amenities etc. I pray for the day there is another Hilton property on Bath Road somewhere (other than the overpriced Hilton LHR at T4)... but that day will be long in coming.