Differences Between Shimano Ultegra & 105 Drivetrains
If you're planning on doing a reasonable amount of Kms I wouldn't purchase anything with less than 105 on it. The groupset tends to reflect the quality of the bike your purchasing. If it comes with a mix of 105 and Tiagra, then it is probably aimed at the recreational rider who might take it out once every other week.

As for 105 vs Ultegra, some parts may make a difference. I don' know the full implications, but I would really take a 105 and ultegra out for a ride and test the shifting speed and precision. I expect the ultegra will shift a little quicker and smoother.

Personally I run SRAM force and love it. It isn't for everyone though as there is only one paddle that shifts up and down based on the length  of your push. With that said, on the cassette I can shift up 3 gears at a time; taking me from 12 to 32T in 4 throws of the lever.

I know in Australia $2k will get you a reasonable bike running 105; and we are one of the most expensive places in the world to buy bikes.