I tend to dress quite casually - unless there's a good reason to do otherwise I'll be in jeans and a t-shirt, or something similar. I'm comfortable in it and I take the view point that in general people shouldn't be making assumptions based on what I'm wearing. Of course they do, and while this can be infuriating at times it can also be amusing. The man at the RBoS who witnessed me signing the personal DD guarantee form for Black Cat obviously couldn't reconcile my appearance with what I was there to do, for example.
I'd never thought about this from the other side until a few weeks ago. I spoke to someone who explained how difficult it had become to conduct business meetings with other companies with the increased level of business casual. In fact on occasion different branches of the same company that he'd be meeting with would have different dress codes, so he'd go to something involving casual dress in the morning and something with full business suit attire in the afternoon and end up feeling over or under dressed.
This isn't likely to make me change my own behaviour in the immediate future (I don't have to interact with external parties as part of my current job). It did help me realise that there was another explanation for awkward behaviour when I'm my usual scruffy self that wasn't just about judging on appearances though.
(All of the above blatantly obvious once you think about it, but it took that conversation for me to do so.)
I'd never thought about this from the other side until a few weeks ago. I spoke to someone who explained how difficult it had become to conduct business meetings with other companies with the increased level of business casual. In fact on occasion different branches of the same company that he'd be meeting with would have different dress codes, so he'd go to something involving casual dress in the morning and something with full business suit attire in the afternoon and end up feeling over or under dressed.
This isn't likely to make me change my own behaviour in the immediate future (I don't have to interact with external parties as part of my current job). It did help me realise that there was another explanation for awkward behaviour when I'm my usual scruffy self that wasn't just about judging on appearances though.
(All of the above blatantly obvious once you think about it, but it took that conversation for me to do so.)

In the geek world, jeans and t-shirt isn't really casual, but strictly formal.
It is the uniform of geeks.
It really depends on your wardrobe. I used to just own jeans and tshirts, or a suit. Now I own a range of clothes which can basically be sorted into 1) trousers including some jeans 2) tshirts 3) "pretty" tops, mostly camisole with matching lace overshirt 4) dresses (strictly for weddings!)
I can turn up in black cord jeans, and a "pretty" top, and be casual yet smart enough not to be embarrassed. I suppose the difference between the two might be a necklace for the more formal meeting.
Similarly why can't you wear semi-casual trousers and a shirt, open at the neck, for casual - then button up and add a tie for formal?
I also think that it's important to be comfortable - not just in a practical sense but comfortable with what you are wearing. I used to have a shirt that I felt awkward in but dragged out for "formal". The tops I wear now are probably technically less smart, but I am comfortable in them and so I think it probably works better or at least makes it less likely that the other party will focus on what I'm wearing.
Hi Flash, fancy seeing you here!
Our dress code here stipulates a lot of things - e.g. trousers not jeans, shirt, tie, shoes not trainers - except for Friday which is casual day but still stipulates a lot of things - no logos, no football shirts....
In practice, I think someone somewhere realised that people are more productive if they're comfortable. Most people here don't wear a tie. Some get away with jeans and trainers. But if you're customer-facing, even just for one day, the full dress code applies.
I actually feel (and people have commented) that I'm more productive on Friday, when I'm comfortable. I also feel that women get away with a lot more than men in a "formal" environment.