it makes no difference if you stay n the same string but if you start changing string you will see the difference.
for example, if you go from high e to b to g strings. you wil pick up the whole way were-as in alternate you pick down on the e up on the b and down on the g.
i would suggest you nail alternate picking before you attempt econimy. the reason being, alternate picking requires little thought after you are competant with it you just let your hand go up and down. whereas you have to think a lot with econimy, and if you are improvising it is easy to get confused. so you need alternate picking at the very least to fall back on.
alternate picking is also easier to keep in rythm, and this is often a problem when playing fast.
hope this helps