It does matter a lot, although to some extent it depends on the type of photography, with portrait shots being the least obviously affected by bad quality lighting and high end still life photography and fashion being the easiest to spot.
Features/spec doesn't really matter (or at least not to me) but the quality of the light does. 'Quality of light' basically comes down to consistent colour temperature and consistent flash energy, so that every time the light flashes it has the same colour and the same power.
Most beginners don't understand this so buy on spec or price and maybe the unscrupulous sellers play on this, knowing that most people not only don't realise how important it is but also have no way of measuring it, and especially colour temperature, which needs a very expensive colour temperature meter.
Maybe some of the sellers don't know enough about flash to know that they're selling junk but some do, and just lie about the true specs, which makes it a bit of a minefield sometimes. Statements like "Colour Temp: 5600k /- 100k" are very unlikely to be true from any seller except Bron or Profoto. And most of the magazines that do product reviews don't spot this because they know no more about studio lighting than the customers, and they don't have any means of measuring the colour either...
Next on the list is accessory fitting. Basically the norm is either S-fit or Elinchrom but some have unique fittings that make the range of accessories (light shapers) very limited and some have fixed reflectors, which is even worse.
After that comes the modelling lamp, because bright modelling lamps are a big help, and the cheap lights that have no cooling fan can't bright modelling lamps.
And after that comes build quality. And it's pretty easy to put a poor flash head in a flashy case and make it look good.
With poor lights used on portrait subjects, you're likely to get every shot looking very different but not realise why. People often take hundreds of shots to get a few that look OK. They don't realise that the problem is with the lights.