It should just be a function of focal length and objective lens size - so all other things being equal the 44mm scope will have slightly shallower DoF than the 42mm scope.
Now having said that, I've looked through scopes that according to the numbers should have worse DoF but they've actually had better - and it doesn't seem to be predictable based on whether it's a fixed mag or a variable mag scope.
The advice most people will give you (me included) is to actually look through a scope before you make a decision - don't make a decision based on the numbers written on a box. There are some obvious exceptions to that though - obviously a 50x mag scope with a 60mm objective is going to have a shallow DoF compared to a 10x42. If the numbers are close, have a butchers through before you part with the folding stuff.
Now something to be careful of when you look through a scope and make your decision. Light plays a big part in this, so try to look through a scope in as many different lighting conditions as possible. Clarity of optics and coatings play a part too and can lead to you think the DoF on one scope is better than another because one just seems brighter and clearer.
The other thing to be aware of is - don't believe the numbers on a box. 10x is a pretty meaningless number - and is rarely accurate (I'm not even sure how to measure it).
But I'll say this - I've had two scopes side by side - both set on the indicated 10x mag and one was very noticeably more magnified than the other. In fact to get the magnification looking about the same by my eye, I had to turn one of the scopes up to 16x mag before they looked about the same. So that's one at 10x and the other at 16x for them to look the same to my eye. (that's a flipping big difference!).
In short - don't trust the numbers, trust your eyes (but not completely - be aware that you might skew any tests in favour of the scope you think will be better without it actually being better), and light will play a big part too.
Edit : typed that while Tench was typing his reply - he's faster at typing than me, or more succinct or both