I am currently running both free trials, with a little more than a week left on HM. They are both awesome. So far, both HUDs are similar and a little better than Elephant's. I am using HM's HUD because I started that free trial first.
HM has more hand filtering options and you can create a player profile of all their hands in one report. They then can be organized according to what moves they've made preflop and on each street. This is awesome and as far as I can tell PT3 cannot do this. HM also lists hands individually. PT3 lists hands, but puts the same starting hands in one group. As far as I can tell, they cannot be viewed separately in list form.
Both have hand replayers and both hand replayers allow you to make notes on each player in the hand that can be carried over into games. PT3 allows you to make general hands notes without having to assgn them to a player. For example, if you think that you should have folded, raised, miscalculated outs, etc. PT3 allows you to make these general notes on individual hands, whereas HM does not, as far as I can tell.
PT3 also seems to be a little more user friendly and has a better feel. Most features seem slightly more convenient and faster to use than those of HM.
But I have read a little about both and there seems to not be a consensus as to which one is better. So even the small differences between the two may make it worth having both. Every tool helps and you will most likely have the right tool for whatever job you need.
All 3 can be run simultaneously and can import hands from each other's HH folders, but I don't know about importing from or running off each other's DBs. I lost my info in the Elephant upgrade.
I am still deciding and trying to figure these programs out, though, so if anyone else has further suggestions, help is much appreciated.