I assume if you are in a drop C or C# you are playing on a 4 string?
+1 on that those are not a "huge" drop for a bass. I wound guess it is probably a few factors:
If you are dropping that E string down to a C or C#, you need to beef that guage up

. IMO, I use a .120T steel on my dropped E to a C bass. But, it never goes back to a E and it keeps that string nice and tight for that C. If you were going from E to C / C to E through out a set, you would probably want something around a .110. Thats just an opinion...
And as other people have said... EQ, cab, and power. Those make a huge factor as well. But one this is for certain, it is a lot like building a high performance sports car. You can't just put on a intake and expect huge gains (unless you already own a Porsche 997TT

) You have to kinda go through the whole system.
I guess it is so subject to taste to why I explain it as such a whole. I'm so OCD on making sure that low is cutting through and just being over critical of my sound (just ask the rest of the band when I'm alway getting something different to play on). It's really funny that when I'm calling it muddy, another bassist or guitarist is like huh
BUT with that all said, I beat you beef that guage up and get you a 410, 412, or 610, you will be impressed