First of all, it's foolish to ask "which one is better?". You're a project lead at TI, so you shld know, these technologies are complementary. A typical embedded system has VLSI components integrated into it. Going bit further we can say there 're no embedded systems without VLSI. Yes, everything can be done inside VLSI .. but it's non-cost-effective & inflexible.
However, the 2nd part of the "debate" .. which field has a better future seems a valid point to discuss. Here're my 2 cents -
1. Embedded systems is a more interesting field, as it sits on top of everything. You get a bird's eye view. VLSI is the core part though. It's a top priority that the VLSI design is perfect, as the whole system depends on it. If you're in the VLSI team, you know the system in & out. However, the embedded engineer (mostly, people who write assembly or low-level code that control the VLSI chips) may not be aware of what goes on inside the chip.
2. If you're an embedded systems engineer & you're sitting in a meeting room with a few VLSI engineers, it'd often happen that you're sitting there sheepishly .. without getting head or tail of what they're talking. It's not true the other way round.If this fact may hurt your ego .. I'd say .. go for VLSI.
3. However, if you're more of a practical guy, you'd go for embedded systems. Fact is, most of the semiconductor companies hesistates to relegate their VLSI design jobs to India. As I said, it's the most important part of the whole system & they want it to be done at home .. by competent engineers. If you're in India, probably you'd be reporting to an American boss, & most of your work will be peripheral. Compared to that the embedded systems guy would have more freedom to work. They trust Indians at the coding part. Your team might be handling the core parts of the firmware development work. So .. if they have to lay off a few guys .. the VLSI guys will be the first ones to go. This may not be the truth if you're actually sitting in the head-office in the US. I'm talking only about the guys in India or other out-sourced countries.
At the end of the day .. you gotta decide for yourself. I'm voting for embedded systems though, because I'm sure if you love the job, you won't feel sheepish in that meeting room.. you'd do some back grnd study & come up smarter in the next meeting at least..