Docking station compatibility for two different dell laptops.

One more thing: Find out the specs and AC adapter wattage of the 5480 you'll be getting.  If it comes with the quad-core processor and discrete graphics, then it probably requires a 90W AC adapter rather than the 65W adapter that's more commonly used with the 5480.  In that case, if you get the WD15 dock, you MAY need to get the 180W version rather than 130W, and if you get the TB16 you will definitely need the 240W version rather than 180W.  The reason I say "may" for the WD15 is that although Dell's FAQ page for the WD15 says that you can use the 130W version with that system because it can pass 90W on to the attached system, I remember a thread where someone found that was not the case with a 5480; he ended up having to get the 180W version.  And interestingly, on the TB16's page, there's more detail about system compatibility, and there's a separate line item for the 5480 saying that when equipped with an H Series processor and discrete graphics, you need the higher wattage 240W TB16 -- although that page incorrectly calls it a Latitude 15 5480 when in fact the 5480 is a Latitude 14 model....

You have at least one, possibly two options.  The option that's guaranteed to work is the WD15, and when using it with those systems, you can get the version with the 130W adapter.  No need for the 180W version.  The WD15 will handle up to two 1080p displays or a single 2560x1600 display (or a single 4K display but only at 30 Hz rather than the standard 60 Hz. 30 Hz isn't acceptable for most users.)

The next possible option would be the TB16, but that requires Thunderbolt 3. That's standard on the XPS 13 9360 but optional on the Latitude 5480, so find out whether your particular 5480 has it.  The main benefit to the TB16 is that it can handle up to dual 4K displays at 60 Hz and even some triple display configurations because it has quadruple the display bandwidth available compared to the WD15.  If you get the TB16, you can get the lower-end AC adapter option, namely the 180W, rather than the 240W version. (EDIT: There's an exception to this.  See next post.)

The D6000 would be the other option, but I don't recommend it because it uses DisplayLink technology for its video outputs rather than tapping directly into the GPU's native outputs, and DisplayLink has some significant downsides.

Also, minor note: It's not an "E"5480.  It's just a 5480.  Previous Latitude models used a letter prefix to signify the type of docking station they were compatible with, e.g .an E5550 was compatible with an E-Port dock and the much older D830 would have used a D-Dock.  With the Latitude xx80 models, Dell removed their proprietary E-Dock connectors on the underside of the systems in favor of industry standard USB-C/Thunderbolt options, and thus the "E" prefix has been dropped.  When I first saw the "E", I began writing a post that you didn't really have a good single docking solution for both systems, until I saw that it was an xx80 system, not an xx70 system. Anyhow, just a bit of Dell naming trivia for you.  Good luck! :)