Shimano 105 v Tiagra
Shimano 9 speed has a different pull ratio to 10 speed.
So this wouldn't be possible.
If your Tiagra is the newer 4700 series - the cabling is routed under the tape - which gives a cleaner line but I found on my Shimano 5700 105 (vs the older 5600 external routing) gave a stiffer shift.

I have found on servicing my cables with lubed and sealed Jagwire - the shifting has improved greatly though.