The Frigate only costs twice as much to maintain (10/turn verses 5/turn), not to build (200 shields verses 150 shields). Also frigates have a higher defense rating (4 verses 3) and has twice the hit points (30 verses 15). (Per the definitions in files "shippak3.SHIP" and "Coreships.SHIP".)
So while you could you would have to build four battle cruisers for the same number of shields it takes to build 3 frigates, but those three frigates can take 90 hit points at a slower damage rate than those four battle cruisers can take their 60 hit points. In theory, you get more battle worthiness for the build cost.
As to maintenance, again, in theory, the frigates excell the battle cruisers, since on average a frigate of 30 hit points at a defense of 4 should be able to out last the 30 hit points of 2 battle cruisers with a defense of only 3.
The cute description of a lot of the definitions of ships, techs, wonders, etc. can be misleading if taken too litterally. Be sure to do a COMPLETE comparison before assuming the supiriority of one thing over another. Then let your experience in actual game play be your final guide.