Wow, what different frogs! Second one looks nice. Check out the link in my signature for tips on taking pics, if you want a good critique. As I said, need different angles to give you much. Also, unless your pics are flipped, the first 2 look like front right, 2nd 2 front left.
Can't tell balance, height, depth or anything very well from those angles, but considering the difference in the frogs - the second foot pictured looks quite healthy - is the first one naturally higher heeled than that one? If so, after you get rid of the thrush, if you're not going to use boots, you might consider using Vettec CS or such on that recessed, weak frog to provide more comfortable support.
The farrier has pared out a lot of sole it seems, in the front half of the feet. While can't tell depth, it appears that the toe soles are quite low/flat/thin & I don't generally like removing sole from around the toe anyway, especially if it's already too thin. Be interested to know how deep the sole is, in relation to the ground at the apex of the frog? Does it yield at all to strong thumb(or light hoof tester) pressure? It sounded like you were saying it did. If the sole is & dropped as it appears it might be, I'd be protecting those feet on anything but soft ground, until they can grow thick.
Likewise, the front of that frog & the other healthy looking one appear to have been strongly pared. I don't agree with routine paring of sole & frog or removing healthy calloused material as a rule, although the thrushy back half of the first frog could possibly have been cleaned out better.
Looks like quarters may have been left a bit long - farriers often just rasp the groundsurface walls level all round - and they're definitely a bit long &/or quarter flaring not addressed on the second foot. This foot also appears not well balanced from side to side, but again, can't say for sure from this angle.
Oh & unless you're in an extraordinarily dry environment, it's not the dryness that's a problem. Chipping & cracks may be due to hoof imbalance, incorrect trimming - may be as simple as lack of a 'mustang roll' in an environment that needs it, infection &/or diet & nutrition problems.