The good Euro frigates are actually pretty expensive and damn near as big as a US DDG.
Everybody here seems to agree the LCS or any littoral ship should have Land Attack, AAW, ASW, and ASUW capabilities along with aviation support.
Challenge is, name a single ship that offers all of the following:
Air defense radar powerful enough to utilize SM-2s...otherwise you've got not much more than point defense against low flying supersonic missiles
VLS system with enough cells to have SM-2s/ESSM, Tomahawk, and VLAs
CIWS/RAM
5 inch gun or better(8 inch/155mm is considered a minimum to engage armor/targets under cover)
VLS...again
SSMs
Hull Mounted Sonar
Towed Array
Sonobuoy Processing System
Helo Hangar+Flight Deck
For all of that, nothing short of a CG offers the whole package. When it comes to aviation/ASW capabilities, DDGs essentially follow the "modular" concept...Flight Is have SSMs, a hangar and a towed array, Flight IIs have helos, but no towed array, many lack SSMs and CIWS as well.
Point is, all that shit crowds up the space on a DDG as it is. Even with miniaturization of the processors, trying to put that on a considerably smaller ship like a Perry size frigate is going to be a challenge at the least. Powerful radars, sensitive sonars, and the like are all space consuming. Then you need generators to power all that stuff, engines to move at a decent speed, fuel to get around...space fills up pretty quick.