On paper, the ships are comparable but use different means to obtain the same end. In the end, I think you are right in saying it will not be an “upgrade” so to speak, just a lateral change in playstyle.
Shield-tank vs. Hull tank - even if you don’t own either of the ships most people know that the FAS is a born-to-be hull tank, while the FDL excels at shield tanking. Because of this, the FAS is slightly less demanding as far as pip management goes, as you can leave SYS at a single pip and drive on.
Speed vs. Maneuverability - FAS is super responsive on the sticks but caps out a little early on speed, while FDL can catch most opponents in a straight sprint, but slides and stalls out if you try to pull turns at full speed, particularly in a boost. Both are optimised for their defensive niches in my opinion, and still require good pip management to ENG in a shoot-out.
Hardpoints - both have very close raw DPS potential but I prefer the hardpoint layout on the FDL.
Utilities - more (6) on the FDL but in practice these typically all go towards shield boosters, leaving one, maybe two for practical purposes. The FAS can make better tactical use of it’s utility slots.
Optional Internals - more on the FAS, but if you are set up for combat, you’ll be stacking HRPs and MRPs out the wazoo. Meanwhile the FDL’s meager amount of internals account for a shield, two banks, a light cargo hold/scoop, and one scanner or interdictor. That’s it, so its mission-running capability is low to just “okay.”
Style - it all comes down to preference, but I love the look and sound of the FDL, it’s about the closest you can get to flying a Ferrari.
Ultimately both are capable combat ships so choosing one over the other really comes down to preference in looks and play-style. Like others have said, get both!