Depends on which Sora and which 105..
looking at your pic they look like 9speed 3500 Sora, which is actualyl pretty good budget kit, works well, slightly klunkier and heavier but good enough.
If you want to go 105 then you’re looking at a jump to 11speed as well (unless you’re going to go for older), which will mean new cassette, chain and mech as well,a nd can your wheels take the 11sp cassette?
Previous two generations of 105 are both 10speed, 5700 is one to avoid for reliability but similar shape hoods/ergonomics to the current 5800 11speed.
5600 105 is similar shape to your current Sora and wouldn’t get you mcuh except a tiny reduction in weight and an extra cog, marginally better shifting (when new).
If you’re sticking 9speed then the old 105 stuff won’t likely feel any better than your current Sora, however…the new 3000 Sora stuff feels pretty damn good for the level it’s pitched at and is simialr in shape to current 11speed stuff.
If you’re constrained by wheels to 10sp or less and want to move to the newer shape hoods/shifters with underbar routing then I’d consider the current Tiagra group (4700), it’s cheap enough and very very good for the money, but you will still need to replace the shifters, mech and cassette.
So the question is; is there a noticeable difference and it is worth the £135?
So In summary, it is noticeable, whether or not you care or prefer one over the other will be personal, and whether or not it’s worth it is up to you. For a commuter personally I stick with what’s robust, reliable and cheap for consumables, which precludes carbon frames for me so we may do ‘commuting bike’ differently, considering mine is metal, weighs a ton, has 38c tyres, and racks at both ends and a trailer hitch we may have different priorities 😉