Since the first Gorshkov is officially in service(and its sister ship the Kasatonov is about to enter testing) to the painful issues with its long range SAM being finally ironed out, it makes sense to compare it to the worlds most powerful and advanced frigate in service
Tonnage
FREMM: 6700t>Gorshkov: 4500t
The FREMM is a much larger frigate
Range:
FREMM: 6800nm
Gorshkov: 4850nm
The FREMM has quite a lot more endurance due to having more crew space and range. The advantage here goes to the FREMM
Sensors:
FREMM: MFRA AESA radar system, UMS 4110 sonar
Gorshkov: Furke-4 Air search PESA, Monolit 34K1 surface search, Poliment AESA, zarya-5 sonar
Since very little information exists on both frigates' sensors, its very hard to make a comparison for them. Both seem to have very advanced Air track capabilities though. I'll consider them equal.
Armament
SAMs
FREMM: 16x aster 15(30km range, mach 3.5)/aster 30(120km range mach 4.5) in VLS
Gorshkov: 32x 9M100(15km range, mach 2)/9M96(120km range, mach 5.4) in VLS and 16x Sosna optically guided SAMs on the Palash CIWS mount(10km range, mach 2,6)
In terms of short range SAM firepower, both frigates are about equal. The Aster 15 is faster and has longer range, while the 9M100 and Sosna are in higher numbers. However the Gorshkov's advantage is that it can carry both both long range 9M96s in its VLS and Sosna short range SAMs, while the FREMM has to choose divide the numbers of Aster 15 and Aster 30s because they're stored in the same VLS.