At first it seems that there is a lot of diference, but then when you practice both then you can see how they help each other.
Some times is not easy to preach people that are in the mode of goodness, yea, because they think that everything that they do is flawless, so most of them become mayavadis or they think that they are Shiva o even worst, Krishna.
The thing is, when you start teaching Hatha Yoga, you teach to them to worship God into every human been, animal and plant, to open their heart to love (bhakti) and to find a spiritual master.
Then by practicing Hatha Yoga they became familiarized with mantra, so is more easy to chant the Maha Mantra with them, at this moment they know the importance of Mantra.
Also Hatha Yoga can help devoties to have a good health, if you are sick most part of time, is hard to make a good service, the fact is not only eat prasad, is eat food offered to the Lord, but if that food is not healthy, then your Sadana is affected, I have seem during many years how many elder devoties have no care with food, but now they have diet, and can not even eat chapati....
As Srila Prabhupada said: if something helps your Bhakti you must take it.
I apologise for any inconvenience if you are not agree with me.