Go with the C4
You only need 4" behind the tank so you are good to go there. Both are made by Hagen/Fluval and use the identical motor (same part #). I have one C4, two C3's and an AC50. There is no comparison in terms of filtering ability and the ability to get canister quality filtration from an HOB. [Both have adjustable flow.]
If you check the official specs, you will see the A/C 70 is rated at 300 gph while the C4 is rated at 254 gph of flow. However, the AquaClear suffers from severe bypass issues due to holes on the side of the media basket so only about half your water is being filtered by mechanical filtration while the C4 filters close to 100%. See this:
http://www.aquariumadvice.com/forums/f60/aquaclear-bypass-issues-292796.html
Out of the box, the AquaClear will not give you crystal clear and polished water because the mechanical sponge is too coarse. About the only way to get the AquaClear to give you crystal clear water is to add tightly packed filter floss.
For a full discussion on this including links to my custom media HOB filtration tab on photobucket.com, please go here and see my posts 29, 35, & 36:
http://www.aquariumadvice.com/forums/f60/hob-filters-301925-3.html
[Edit: I see you've been on this forum for four months with 270 posts so I don't have to tell you probably most experienced members would not think a single C4 or AC70 is sufficient filtration for a 55 gallon tank unless it is lightly stocked.
On my heavily stocked 38 gallon, I run two C3's at maximum flow and an AC50 as an auxiliary filter at less than "half speed." On my moderately stocked 29 gallon, I run one C4 at about 2/3 maximum flow because angel fish and Dwarf Gourami seem to prefer less "flow."]