I want to play some bachata lead guitar, and want to play the same chords as the rhythm guitar. However the chords are on the bottom 3 treble strings on frets 10 to 15. I am not familiar with these voicings.

For example if the rhythm guitar is playing E major. Should I do an F position barring the 15th chord.

In effect this is an E/F# as I am only playing the bottom three strings. Or should I do a chord which makes the 3rd string an E?

I have no idea which would sound better or which is correct.

Any tips to help me make this decision?
yeah, i think you should use fragments of barred chords to achieve this. to use your example a high E barre chord:

e -12---
b -12---
d -13---
g -14---
a -14---
E -12---

if you're only using the top three string, all you need is this:

e -12---
b -12---
d -13---
g -------
a -------
E -------

so figure out where the full barre chords are for where you want to play, and strip them down so you only fret the notes on the strings you play.
hope that helps you
what you're looking for are triad inversions on high 3 strings. Look for those on web and you'll find all the right fingerings and all that stuff. plus it will help you unlock guitar neck, so you'll know what's going on there. really cool thing to know.