I lived in Austin for many years, as well as other parts of Texas, and still visit when I can as I have extended family and friends there.
Austin is not at all like other parts of Texas; it's an entirely different place. I don't know if I ever saw a pair of cowboy boots, big hair, or dolled up women in Austin, and I never saw much jewellery or even vanity there at all. It's a VERY laid-back, music-oriented, quite hippie sort of town where half the people have dreadlocks and massive holes in their earlobes and the other half are engineers in jeans and nerdy t-shirts.
All of the weddings I went to in Austin (loads!) were men in just khakis and shirts, women in simple, fairly casual dresses - IME either of the frocks in your OP would be fine for any of the Austin weddings I've been to. I particularly like that colourful first one and think it would fit in well.
However, the answer to your question is going to depend on what type of person YOUR FRIEND is and some things about the wedding itself, as Austin takes all sorts!
- Is she very wealthy? Will she have wealthy friends/family there? That could mean different expectations.
- What age group are the party in? That could make a massive difference.
- Where is the wedding? A hotel? Ranch? Park? Home? Event centre? Do you know the specific location (and care to share)?
- Is it in Austin proper or a suburb?
- Is it day or evening? (I assume evening, with "cocktail" dress code?)
- Indoor or outdoor? Or possibly both?
- When is the wedding; what month?
- Do you have any hint of a theme (maybe from the invitation)?
- Have they given any other information about the reception in the invitation?
In the end - unless they are really wealthy types who have their own set of etiquette that I just don't understand - most likely nobody will give a toss what you're wearing and will only be genuinely happy that you were able to make it, especially from so far away. And your accent will be a novelty and everyone will want to speak to you, so prepare for that.
Though as pp have said, do keep in mind that it is very, very bloody hot in Austin in summer. You cannot imagine the heat. It's oppressive and can even be frightening. If you bare your shoulders, SUN CREAM THEM! And maybe dress up your frock with a large, floppy hat for extra shade! However, the AC is indeed vicious (brilliantly said), so pack a cardi and take it with you to the wedding just in case!