What to open with KJxx Kxxx AQx 32? If you play a 5 card major system you have either the choice to open those 4432 hands with 1 (you have to alert it) or you play any minor from a 3+ card (you don’t have to alert it). But to open this hand with a club, it's plain ugly.

If you open 3 card minor you can bid inverted minors with only a 4 card support and find out what partner had. If an opening could have a doubleton club you need at least 5 clubs for inverted minors.

With weaker hands and only a 4 card support you just bid 1nt. The most likely contract you would end up regardless the opening. But with a weak hand and a 5 card support you can jump to 3 level in both clubs and diamonds if partner has at least a 3 card.

With better minor you can support with a weak 4 card at 2 level and at 3 level with a 5 card in competitive auction. With only a doubleton clubs you have lesser opportunities to support clubs.

Some figures and statistics  Better Minor, Worst Minor or Random Minor.          

If you open 1 (with 11-14) with a doubleton it will happen only 8.5% of all 4432 (11-14) deals (2.5% of all 4432 deal / 0.5% of all bridge deals). In those 8.5% you have:
a 8.8% 5-2 misfit in clubs (included the 2.1% you also have a 43 misfit in diamonds). We are talking about 35 hands in 100000 deals.
a 15% 4-3 misfit in diamonds (also included the 2.1% you have also a 52 club misfit
in 11% there is only a 33 fit in diamonds
in more than 60% there is a fit (4.3% 6-2 fit in clubs, 14% diamond fit and 42% major fit)

After a 4333 opening you have a 18.4% chance of a misfit in clubs or diamonds (included the 5.2% double misfit), but you also have more often a real diamonds compares to clubs (16.6 % vs 15.6%)

Since there is a better change of a real fit and a greater change of a smaller minor misfit my conclusion would be that it's better to open with a 3 card minor. Besides that you don’t have to alert a 3 card minor opening en the opps are less likely to inter-vent your 1c opening (there are a lot of conventions in use to co-op with unreal club openings).

Another advantage is, you don’t' have to consider the fact partner has only 2 clubs, in competition you could easily support with a 4 and 5 card support. You also do not have to protect your partner with 1 spade with a hand like QJxxxx xxx xx xx you just pass and wait. The fact that your partner could have a 3 card should not withhold you from supporting with a 4 card. If you play 15-17 NT you will end sometimes end up at 3 level in a 4-3 misfit and go down and it will cost. If you play a weak NT you are protected by the system, partner will always have a strong NT if he has a 3 card. One more reason to play a weak NT.

In Better Minor you open your best minor, in Worst Minor you open your worst minor, both have the disadvantage off showing weakness to your opponents. In Random Minor that problem is solved. You just pick one. But what to pick? If you have a good suit like AQx or KQx you will open that one, you could withstand a lead in that suit. If you have hands like Qxx or Jxx you would not want the lead and you open the other minor. With a 18-19 NT it is considerable to open your worst minor to avoid the lead in that suit since it;s most likely you would play the contract.