FWIW: IMHO, I'd say...
Out of F1 '14 and '15 - there isn't really one game that is a complete game within a modern package - '14 & '15 are obviously more up to date with the new(ish) engine / power unit formula, but are worse games than '13 which although uses the old engine formula is otherwise a better game. So no matter what your choice is, your modern F1 racing needs will probably feel unfulfilled. In a nutshell, I'd ask yourself if you're more concerned with gameplay or playing with the modern formula - if it's the former then stay with '13, if it's the latter then the choice between '14 and '15 is more dependant of a few matters...
Controller type:
If you're playing with a gamepad then F1 2014 is the worst of the 2 games as Codemasters applied a horrible driving aid type type handling model for controllers only resulting in restricted and underwhelming car response / gameplay. If you take it as it as, you can still have some fun, but it doesn't feel like you're in full control and consequently has a more arcade aura to it. F1 2015 seems to also work better with wheel and pedals than gamepad, but even though the gamepads usability is better than '14 handling with less hand-holding, '15 model has a more vague and disconnected feel, which is a bit weird at first. Once you get used to it, and with some finetuning of the controller settings, you can get a handling system that feels more like "simcade" - part simulation, part arcade. The cars feel more sensitive and can easily be spun-out or wheel-spun within corners, so it's more challenging than '14, but you can never push 100% as the moment you go to 101% (which you never feel the limit of grip approaching) it'll spit you off the track like Nico Rosbergs real life moment towards the end of the USA GP. F1 2013 has the best of both worlds and has a very controllable and usable car controller system and you can push it to the edge, so I'd say '13 is the winner here.
AI:
F1 2013 and '14 both suffer from obvious rubber-banding, as in the AI's pace is established according to your pace. If you take a corner badly the car if front won't shoot off into the distance, it'll slow down so that you can have some false entertainment. '15 doesn't seem to have this, or at least I haven't noticed it, so that's an obvious improvement. There was a common issue with AI overall speed where Legend was generally too fast and Expert (next setting down) was too slow resulting in imbalanced gameplay, which seems improved in '15 to the extent where Legend is now playable and seemingly realistic in terms of pace. '14 has the same or similar AI model to '13 - the opponents don't put up much of a fight in both attacking for an overtake or when defending from one, leaving battles quite straight-forward. F1 2015 has much more stronger AI, that'll attack and defend at the slightest opportunity, but their aggression can be OTT at times to the extent where you really have to consider your car placement and general surround activity a lot more than ever before, and your wing mirrors very much become your closest friends. The "better" AI out of these games will simply be a matter of preference, if you want decent if unspectacular AI then '13 and '14 are your choice, or if you fancy AI that'll be both more fun yet occasionally more frustrating then play '15.
Game complete-ness:
In terms of content, simply put, the later the game the less content is present. '13 was feature packed, '14 was more bare-bones, and '15 is arguably incomplete due to the omission of a safety car and personalised career options. '15 was, and currently still is buggy to the extent of being partially broken - I've seen plenty of example where fundamental gameplay errors (mainly orientating around race strategies) occur. Yesterday I was attempting a 100% distance race in '15 around USA, which started during light rain on intermediate tyres, my scheduled stop was lap 18 but by that time I saw the sky getting more blue, the rain had pretty much stopped, the race engineer said we could go to dry tyres if I felt I could keep it on the track, so I stayed out 3 more laps on dying inters to wait for the perfect time to switch, excitement was very much on the up, I pit thinking I'd responded to the situation as best as possible, and despite my specific instruction to stick on a set of prime tyres they slap on a set of inters again. I go out, struggle with a drying track for about 2 or 3 laps then simply quit the race as it was now completely ruined for no good reason and for no fault of my own. For crap like this, I can't recommend '15 as a complete and functional experience, so '13 and '14 equally win out here.
Performance:
If you're playing on PC then just be prepared for the fact that F1 '13 and '14 engines run at seemingly identical levels, but '15 requires a lot more GPU power to run on max settings - you'll need approx 3x raw performance capabilities and 3x more VRAM. '15 isn't optimised anywhere near as good as '13 and '14 to the extent where my GTX 780 (or near equivalent, the popular GTX 970) struggles to maintain a solid 60 fps @ 1920x1080. It would be more understandable if '15 looked significantly better than '13 or '14, but in my opinion it doesn't so it's an unfair trade off that ideally needs improving. 2015s replays and some brief cinematics are limited to 30 fps, but can be unlocked to 60 fps (or more) is you disable in-game v-sync and enable it via your GPUs control panel (NVCP or CCC). For these reasons, '13 or '14 are the better overall choice (unless you're running a powerful pc).
Audio:
Although not of massive importance, '15 occasionally suffers from poor if not buggy audio implementation for surround sound users - notably during replays. It's not really a game breaker but the mix when watching from "tv cameras" is a complete mess. As for general engine sounds, both '14 and '15 aren't particularly realistic and / or good, which combined with the new engine / power unit system results in a very average at best result. Personally I way prefer the sound in '13 for both its high revving nature and general sound authenticity and quality, so I'd say '13 is the best in this category.
Ultimately, I now play all 3 but each for specific reason - if I want to focus on tough racing with the AI I'll stick on '15, if I want more relaxed but fun(ish) and modern setting gamplay then I'll stick on '14, and if I want just an all-round fun and complete F1 game then '13 is the winner.
EDIT:
A few hours after writing the above, I revisited F1 2014 and pretty much immediately lost interest purely due to the over-assisted car handling (car in the wet was able to do lots of full throttle while a hidden traction control type system was in effect, making it very unrealistic and equally unchallenging). So I setup a 50% race in USA on 2015, and I was actually able to complete it. I initially set the AI to Legend but qualifying times were too realistic in a stressful manner, so knocked it back expert which was a more comfortable challenge and level of fun for me. The race generally went well, but I noticed a few "areas for improvement"...
- Race Engineer audio has been EQ'd in a horrible manner rending the audio as complete gibberish (FYI: I have a Room EQ'd calibrated home cinema setup with a centre / dialogue speaker accurate to 0.5 dB - so it's definitely the game at fault here). I ultimately had to enable subtitles to understand what was being said, which is obviously far from ideal).
- AI is generally very good, but they all have a weak spot where if you dive on the inside within a corner, typically while under braking, they'll see you and simply "open the door" and give you plenty of room to pass. They're hard as nails though in any other racing situation.
- Back-markers are dangerous as hell - you'll encounter one and they'll continue to race at their pace until they decide to let you pass upon which they'll immediately drop the anchor and hope for the best. I had two occasions of back-markers suddenly parking up right on the apex of 3rd gear corners going at 1st gear pace, both of which I hit and even received a warning for doing so.
- Pit activity: one curious occasion I entered the pit with Hamilton immediately behind myself, my garage was slightly ahead of his, I was stationary for 2.3 seconds - yet he jumped me somehow. I didn't have to wait for release so don't know how that's realistically possible.
Overall though, I actually mildly enjoyed the experience, and would now say that 2015 is better than 2014 in their vanilla (unmodded) states, but I never got that much into modding '14 other than my camera mod so don't know how far that could be taken. Is '15 better than '13? Not quite - it's just not as fun as '13. Is it worth buying '15? I'd say, now that's it's cheap enough (providing you know where to look) then yes buy it, but keep your expectations in check and expect a decent title that steps in the right direction from 2014 while demonstrating the potential for an excellent future title.