While I have never stayed at any of the Hiltons at FRA, I've had some really negative experience during my last stay at the Sheraton due to poor handling of an overbooking situation. Speaking for myself, I would probably try the Hilton next time.
As far as club rooms at the Sheraton go, their size is ok, and all of them have been refurbished a few years ago. However, the bathrooms weren't up to date anymore (not sure whether they have changed anything about it), and the offerings in the club lounge had been better a few years ago. It's probably really a matter of taste, however, the difference in walking distance is really negligible, as no matter where you stay, all walkways are covered and equipped with travelators. The difference is probably something around 200 to 300m, particularly if you're heading towards CI A (not sure where SQ do their check in, but I believe it is somewhere between A and B).
Addendum: when it comes to food, both Sheraton restaurants (the local one is very well hidden below ground level somewhere among the conference rooms) seem quite overpriced - but with the full choice of food options at FRA (including the Squaire) that shouldn't be a problem. And if you're only looking for a small snack, you might even be inclined to check out the hot food buffet at the REWE supermarket in the Squaire, on the opposite side of the building when seen from the Hilton.