I have more experience in El Chorro that the Costa Blanca, and the latter experience was in Sept. (too hot) not winter, but can offer a few comments. The Costa Blanca covers a MUCH larger and more spread out geographical area than El Chorro. While 'El Chorro' (as described in the Rockfax guidebooks) does include a number of other crags, most of the described climbing is located on one escarpment--most of it reachable relatively easily on foot from lodgings that are located in a relatively centralized area. The Costa Blanca (again as 'defined' by Rockfax) has numerous crags spread over parts of at least 2 provinces, some of them one or 2 hours drive from others, with no one single crag (with the possible exception of Sella) being a 'destination' in and of itself. As the crags are so spread out, so are the accommodation options. You specifically mention the Alicante area, which does offer a decent concentration of crags within reasonably close proximity of each other (though quite a few of them have been popular for years so suffer from significant polish--which I didn't find to be a major issue on many of the El Chorro routes that I've done). What is worth noting about this area though, is that it is along the coast and as such, is extremely (excessively) built up in many areas and largely full of British and other escapees from the northern winter--particularly around Calpe and Benidorm. This means that there are plenty of accommodation options, but it is a very different experience than the rural back water of El Chorro. There are undoubtedly other accommodation options deeper into the interior, though these would likely require longer drives to get to the various climbing areas.
I have been informed that, despite being further north, the Blanca actually has better winter weather than El Chorro, but on one of my early January trips to Chorro we were enjoying the winter shirt sleeves weather while friends not much further north were sitting out days of cold rain. Unfortunately my most recent trip to El Chorro, this past March, saw us dodging the rain most days--though it wasn't any better in the Blanca.
I'm sure that you'll find a good place to stay, plenty of fine climbing (if you are willing to drive a bit) and, hopefully, good weather if you decide to check out the Costa Blanca, BUT there will be a new El Chorro guide out this fall with lots of additional routes to tempt you to return there.