In my experieice, there are two issues to ocnsider with bicycle components - features and quality. While a lot of the features 'trickle down' from the higher groups to the lower ones, the quality does not. For instance, a set of 1993 7 speed Deore XT components is still better than a set of 2012 9 speed Deore components because the XT will have better materials and suffer more use and abuse before needing replacement (better quality), even though the Deore is 9 speed (more features).
However, the difference between 105 and Tiagra is very slight and a 105 derailleur with a bit of wear in the pivots will likely be a bit more fussy to set up and keep adjusted than a brand new Tiagra replacement.
When new they all work almost the same - you likely could not tell the difference between Tiagra and 105 or Ultegra when new. Even if you could discern a difference, it won't make a difference to the way the bike rides.
Unless your 105 stuff is damaged or totally worn out (the derailleurs - the shifters tend to not wear out so much as occaisionally and suddenly 'fail') then it can be set up to behave almost as well or as well as the Tiagra stuff. Newer != better.
If you have a working set of 105 components 'upgrading' to Tiagra will be a waste of money. New cables, chain, cassette, and possibly derailleur jockey wheels will make the bike work like new.