In comparison the two designs are the same, but very different. Yes they both say subway, however they giving off a different message. This is all very subjective so be warmed. The design on top is saying "look at me". Obviously its saying subway, but the heavy outline and italics are just crying for attention and approval. You cant not remember this design. Is that good or bad though?
The newest design is anything but new. This was the original design that was used when the company first began. Not only is it simple in type, but color and overall design as well. Its gets the point across with the subtle colors. Rather than begging for attention its saying " well we have good cheap sandwiches if you want one".
A trademark can make or break a company. Look at McDonald's, when seeing that over sized M on a red background we all understand exactly what that means and who it is. I think that with the right advertising and marketing subway could achieve the same level of popularity. In this new trademark, we can see a relation to the Gestalt principle, Law Of Closure. There are two over sized arrows that create an S, then suing the negative space we can see another S. Creating some what of an illusion for the eye.