Aaaaalright this deserves some discussion. Just because you’re trimming out pitch rate does not mean you’re in direct control of the jet’s flippers. Fly-by-Wire (FBW) does not equal digital controls or even a flight control system (FLCS), necessarily, and analog does not imply pure hydraulic or mechanical linkage. FBW just means that instead of the stick being linked to the flippers by physical means it sends an electric signal which makes an actuator move somewhere. Frequently that means the signal will go through a computer and be altered in some way to make the jet fly better (or be controllable, period) but that’s not NECESSARILY the case- IIRC early Boeing jetliners had electrical lines going to the control actuation systems (CAS) with the yoke receiving mechanical feedback based on sensed panel loads. In English, the pilot feels like he’s got a direct line to the flippers but it’s actually simulated by the yoke itself.
What most people associate with “FBW” is a FLCS much like the F-16 which is a fly by wire digital flight control system (EDIT 2: actually in earlier blocks, this was analog, later blocks went digital, more on this below). In essence you’re not ‘flying’ the jet, you’re providing commands to the flight computer which continuously moves the appropriate flippers the appropriate amount to try to meet the input you have commanded. The “on rails” feeling you get from something like the F-16 or Mirage comes partially from the “tracked statistic” of the FLCS which is nominally Z-axis acceleration (eyeballs up/down) limited by both the max safe number of Gs and a maximum safe angle of attack (alpha) in the pitch channel, generally scheduled at least by mach and altitude. There’s more to this though, in that because the pilot’s command passes through the flight computer, it can shape the aircraft’s response to that command which can be tuned to be fast, slow, efficient, gentle, whatever. With mechanical linkages or direct control the flight computer is your brain- you’ll make continuous little movements to adjust the response to your liking. With the digital FLCS the experience is typically a lot ‘cleaner’- it doesn’t need to be, but typically this is the design decision made for what are hopefully obvious reasons.
When we look specifically at the first 4th generation jet fighters (like the F-14 and F-15) we see an interesting version of this in that you have hydraulic flight controls augmented with mechanical or analog stability assists working in parallel with a FLCS providing “stability augmentation” (at least for the F-15, haven’t studied the 14 as much) known either as a stability augmentation system (SAS) or control augmentation system (CAS- I know. Same acronym as control actuation system. Welcome to engineering.) I actually don’t know if the F-15 CAS is analog or digital- @klarsnow? Now, the Eagle is perfectly capable of flying with the CAS off, and the jet will still try to trim for zero pitch rate, and furthermore, pulling on the stick is still commanding Z-axis acceleration. The hydraulic controls are set such that for a given mach/altitude the gearing hooked up to the stick will approximately give you X G’s per Y lbs of pull-back, while the pitch trim compensator will still try to set the jet’s pitch axis to hold 1G constant in level flight.
So the question is: if the controllers of the Eagle and the Falcon are both trying to do the same thing (here’s a stick input by the pilot, translate that into commanded Z-axis acceleration in the pitch channel, translate that into the right flipper deflections) why do the two feel so different in practice?
Well. That’s complicated.
But we can generalize it into two buckets: feedback and system bandwidth. Feedback refers to a control system adjusting its response as it goes based on data about how the response has performed so far. Bandwidth roughly means the speed at which a control system can adapt to change or disturbance. This is where things get a little complicated. On an all digital FLCS the flight computer is continuously adjusting its response based on input from the jet’s sensors. Generally, for at least acceleration and rotational rate data, this happens quickly enough that the limit of how fast the FLCS can adapt is the speed at which the servos can move the flippers (given that mach and altitude aren’t rapidly changing). That’s not necessarily the case with hydraulic systems. Take the F-15: the pitch gearing will adjust based on mach and altitude to try to meet X G per Y lb you pull, but it’s not actively changing to correct its response. The pitch trim compensator is trying to adjust to maintain X G per Y lb of pull, but it’s adjusting trim, not responding (accurately, at least) to disturbances. That’s the pilot’s job! In general the bandwidth (read: ability to respond) of the mechanical components of the hydraulic controls aren’t fast enough to get rid of disturbances, and you’re in for however of a bumpy ride the aircraft’s aerodynamics dictate. (See Edit 1)
But remember: the Eagle also has its CAS, which IS accepting digital feedback and CAN respond fast enough to remove disturbances… at least to the extent that the Eagle’s mixing logic allows the CAS to alter the hydraulic system.
So: What’s the point of this unnecessarily long rant on flight controls?
Circling back, the Su-27 feels “analog” because that’s how its FLCS is designed. If the DCS manual is to be believed, the Su-27 pitch channel accepts stick throw which is corrected to a consistent pull with aero data (similar to the F-15’s pitch gearing), which is augmented by the “autostabilizer” and the “damper”. The autostabilizer takes acceleration, alpha, and rotational rate data and prevents you from aggressively departing the aircraft. The damper takes rotational rate data and prevents you (or disturbances) from making things change too fast and then leading you on a trajectory to depart the aircraft. NOTE: there’s no “automatic trim compensator”.
When you flip the “cobra” switch (Automatic Stability Control Override) you bypass all of these- the stick throw to fin deflection becomes constant and the only thing adjusting input is your hand, allowing you to do things like purposefully depart the aircraft and then use your crazy pitch authority to bring it back, like in Pugachev’s Cobra.
So, long story short, the Su-27 feels wild and alive because hey, that’s how they designed it. FBW aircraft can be fun too. 
EDIT 1: This is not entirely true- you can absolutely have stability augmentation and feedback using mechanical systems, but response tends to be slow. You either need a stable airframe, or an unstable airframe that departs s-l-o-o-o-w-l-y. The whole point of putting in FLCS systems in fighters is to enable relaxed in flight stability and unstable or neutraly stable airframes for agility.
EDIT 2: throughout this piece I’ve been referring to “Digital” and “Analog” flight control systems which isn’t exactly accurate- analog electronic flight controls can perform closed loop flight control just like digital ones, with the difference being primarily in the electronics for the purposes of what I’m explaining here.
I think the list of IT support people who’ve been able to do that is VERY small!
it happens!