The 5110 made its appearance in 2000 and was replaced in 2006. The Travel Time 5134 arrived in 2001 and discontinued in 2008.
The 5110 is a world time, which means that it gives the time of 24 cities in the world, while the 5134 is a Travel Time, giving a second time zone which can be se forward or backward, at the contrary of the 5110.
The cases have the same shape and dimensions: 37 mm, but the 5134 has two pushers on the left side ( to set the second time zone ).
The movements are not the same: Automatic, Cal 240 for the 5110, and manual, Cal 215, for the 5134.
The 5134 lived under the shadow of the 5110. Ok, these are not totally the same complications, and we could also say that with its second time zone adjustable forward and backward, the 5134 is more practical when you travel, but the 5110 has such a poetic and romantic character, as well as an iconic status.
I made my choice, which is well known, here.
What about your preference?