Is a 1 hormone low dose birth control less effective than normal birth control?

That's a good question!!

Ok, here goes:

Progesterone-only pills have a slightly lower efficacy rating than a combination pill, which is to say that under PERFECT circumstances, combos have a .1 failure rating, while progesterone only has a .5 failure rating.   (This means that out of 1000 women using combo pills, one would become pregnant in one year, whereas 5 would become pregnant using the mini-pill).

In real life however, they both have an equal efficacy rating of about 95%.  
This means that if 100 women each took progesterone only or combination pills, both groups would end up with 5 pregnancies at the end of one year.

The most important thing to remember with the mini-pill is that it needs to be taken at EXACTLY the same time every single day.  That is the drawback to this type of pill.  If you miss a pill by a few hours, the percentage of coverage drops a bit.  If you miss a pill entirely, the coverage drops precipitously.

Are you on the mini because of other concerns besides birth control?  If so, then I'd stick with it.  If not, you should talk to your doctor about options of low-dose synthetic estrogen combination pills like LoEstrin or Yaz or Yasmin.

Good luck.