I owned both at the same time and only sold the CA-1a because I've not won the lottery (yet!) and because I like to have a collection of headphones that scratch different itches. The particular itch I needed scratching was better served by the SR1a, although this isn't to detract from the exceptional quality and relative value (vs other totl headphones) of the CA-1a. (Making the CA-1a even better is that you essentially get two different headphones thanks to the pad rolling options).
For reference, here's how I hear the LCD-R. These headphones offer a pleasingly smooth sound, one that comes with a lovely combination of good resolution, for the price, excellent speed and nimble responsiveness from the drivers, with nicely responsive transients, very good microdynamics, and a decent amount of punchiness. They’re invitingly mellow, engaging headphones. The treble's very nice, if a bit polite (as in rolled off), and the tuning has a pleasant warmth and a delightful sweetness to it. On the other hand, the LCD-R doesn't offer the best bass presentation. The bass doesn’t extend very deeply and could be more robust. It has some good mid-bass punch - which gives the LCD-R its warmth - and, like the HD 650, the LCD-R edges towards being slightly muffled and congested (or “intimate,” to put it more politely). The bass could be tighter/faster, which makes it come across as slightly indistinct and woolly. The LCD-R aren’t as open and spacious in their staging as I’d like.
The CA-1a and LCD-R share only a few things in common. They both have fast transients. The CA-1a's attacks are faster, snappier, a bit more aggressive. The LCD-R's attacks aren't all that far behind but they have slightly less edge to them. They're gentler.
With the donut pads, the CA-1a have a warmth to their tuning that gets closer to the LCD-R, but the CA-1a is still not as warm as it has more treble extension and emphasis and a more linear bass, which is tighter/faster and extends deeper.
The LCD-R have richer, more forward mids. The CA-1a with the coffee bean pads have more of a studio neutral kind of tuning, with a pretty even frequency response, as in no single part of the FR really stands out above the others, although I did find the treble to be a bit more emphasized and, at times, a bit zingy or hot. Then again, the CA-1a have more air.
The CA-1a has a lighter tonal weight and can be a bit dry. Its other distinguishing qualities are its greater openness, its spacious staging and precise imaging, as well as its excellent clarity/transparency, by which I mean there's little by way of coloration to the sound. The LCD-R, by contrast, are warmer, wetter, more mellifluous. The LCD-R make for a mellower listen, one that's immersive and sweet and pleasing. The CA-1a make for a more exhilarating experience, one in which you're drawn into all of the details in the music. They work well together, as contrasting headphones that can be entirely satisfying at scratching those different itches.