Rahnooo,
I compared the Minimat and First Lady recently when I visited Matamp.
The First Lady is indeed an evolution of the C7, but with two different (switchable) output valves, a Voice knob (thick and bassy to thin and wiry) plus some other additions.
While they're both "low wattage" it's important to realise that all Matamps are underrated in terms of powere. Matamp measure them at the point the clean sound ends, so the First Lady is 7w clean, but 20w at full distortion. That probably makes the Minimat about 5-6w max - it's certainly louder than you'd think.
I thought the MM was pretty similar in terms of sound to the FL when the 6v6 was selected, although the MM had a bit more distortion. Switching to the 6CA7 valve on the FL (similar to an EL34) gave more distortion and more of a Marshall vibe: a snarlier, more aggressive distortion, ideal for classic rock.
I loved them both, but couldn't attenuate the FL down enough when it was distorted - I mostly play at home volumes. So I ended up ordering the MM. It hasn't arrived yet, but I keep dreaming - literally - about it. I haven't ever heard a low volume amp sound that good.
If you want a lot of dirt (heavy rock / metal territory) neither amp will satisfy you, but for clean / blues / classic rock they are awesome.
A couple of extra things about the MM that make it a lot more flexible than it first seems: (1) the Low Input is designed to take pedals well, so you could put your UberMetal or whatever in here and rely on the MM to give you the valve warmth and (at higher levels) power amp breakup; (2) the DI from the MM is designed so you can plug it straight into another, more powerful amp and get similar tones at much higher volumes. Effectively you're using the MM like an overdrive pedal or preamp.
There are reviews of both amps in this month's (February's) Guitar Buyer magazine. I'm told by Jeff at Matamp that the editor of GB visited and was so impressed he walked away with a Minimat, First Lady and King Street for his own personal use.
Rahnoo - I just noticed you're based in York. You've got to visit the place - Phone Jeff and arrange something!
