Without You Here - your tempo is a bit slower but, more importantly than that, your backing track is using longer note durations than Fisherman's Horizon. Horizon uses a lot more 8th note arpeggios and your piece is using a 1 & 2 3 (half note here). So half of your measure is already four times slower as the 8th note pace (if you go from 8th up to half note duration). Even if you had exactly the same BPM setting, your piece will feel slower just with that difference in the arrangement's rhythm. Later on you do have some 1 & 2 then quarter notes on beats 3 and 4.
Also the timber of the synth patch you're using is set in a lower octave and has a darker sound than the FF8 reference piece. Your piece also feels more reflective and introspective to me. Almost even melancholy. Whereas the FF8 reference track is more peaceful and uplifting. I think this is partly because of the chordal progressions and resolutions used.
Your piece, by itself, sounds good but I don't think it's a good pairing for trying to recreate the same mood as Horizon from FF8. Maybe take a look at the various parts/elements I mentioned and if you want, make an alternate version where you make some tweaks to better match up the song's mood with your reference track.
Best of luck!