Depending on your source and your cost, it might be better to switch to modern Tiagra (10-speed) than older Ultegra. if you can get old Ultegra super cheap, I guess, but a few hundred bucks gets you a lot of good gear at Ribble or Merlin.
At Ribble cycles : Shimano Tiagra 4600 10 Spd Double Groupset ----- From US$262.11
For $262 you can have brand new full Tiagra 10-speed double---everything from chain to bottom bracket to brifter, cranks and cassette and derailleurs ... even brakes. Basically add a frame, saddle, seatpost, stem, and wheels and ride away.
EDIT: Whoops, sorry while I was typing all that you answered about having usd Ultegra on hand already.
Which bike fits you better? Which one do you enjoy riding more? Upgrade the best one with the best parts ... but idf you already have Tiagra on a bike you like, i doubt you'd be a lot happier switching unless you enjoy doing the work.