How close is X-Plane experience to real flying?
X-Plane is a much truer simulation of flying than that flight game Microsoft used to make. In fact, when coupled with certified hardware and a CFI, X-Plane can power a sim that you can actually log FTD time in.

Since you ask about airline flying for your comparison, there is a lot more to that than just the flying. An airline pilot is, with few exceptions, always operating under instrument flight rules (IFR). This means flying in the clouds with no reference to anything but instruments, weather as bad as a few hundred feet visibility and strong crosswinds for landing and takeoff are all part of normal ops. You are also operating under ATC, so radio ops are normal. The only comparable computer simulation of ATC to reality is VATSIM (as mentioned in comments), though it doesn't approach the level of busyness that you'll find in some airspace and airports (with the exception of some of their organized fly-ins).

A transport category jet is also a bit more complicated than "turn the engines on, release the brakes and go". The only computer sims that capture the level of detail properly are ones like the A-10 simulator by DCS. Before you can start the engines, you need to first power the aircraft and perform your receiving checklists, and if you are the first flight of the day, additional first-flight checks. These cover:


Thorough pre-flight walkaround inspection
Powering the airplane on batteries
Transition to ground power (GPU) or start the APU for power
Verifying the state of all systems
Fire test
Stall warning test
Anti-ice system test
Checking oxygen levels and masks
Autopilot test
Backup instrumentation checks


Before pushback:


Verifying fuel load
Get load information from flight attendant/gate agent/dispatch/ramp supervisor
Calculate weight and balance, move passengers and/or bags if needed
Get ATC clearance and program FMS
Flight crew and cabin crew briefings
Weather briefing 
Start APU and disconnect ground power and ground air conditioning
Get clearance for pushback


During pushback:


"Before engine start" checklist
Set bleeds / packs for engine start
Communicate with ground crew for engine start


Now you can start an engine. Unlike a small airplane where you start the engine by turning a key in an ignition switch, in bigger airplanes its a series of knobs and buttons to press, sometimes dependent on certain events during the start. Engine parameters must also be monitored in case an abort becomes necessary.

At this point you can get a taxi clearance and start moving toward the runway. You'll go through a couple more checklists, "after start/taxi" and "before departure", to prepare the plane for taxi and takeoff. Once you are on the runway, with all checks completed, with more fuel than your minimum dispatch release, and an ATC clearance you may then release the brakes and go flying. One pilot will fly and the other will monitor instruments. 

Much of the above is beyond the typical scope of X-Plane, though some can be addressed with specific aircraft add-ons, manuals and software like VATSIM.