Using a 125 grain vs 100 grain head on a crossbow bolt modestly increases the Front of Center (FOC). At typical crossbow ranges of 15 to 40 yards this improves accuracy. A heavier setup is also less susceptible to wind drift. Heavier setup is also a little more forgiving if you hit bone.
In terms of how i selected my 125 grain broadhead i like one that is completely monolithic with fixed blades. By this i mean completely machined from one piece of steel. Most fixed blades are attached to the shaft of the broadhead by some type of mechanical means. A monolithic broadhead will always be stronger than one comprised of several connected pieces. There are pros to having the broadhead constructed in pieces however in that a damaged blade can easily be replaced.
When all is said and done though these are deer we are talking about not grizzly bears and a 100, 125, or 150 grain broadhead of just about any design will work fine if you can accurately hit the vitals.
Going up a step to 150 grain heads basically ups every benefit except it further reduces bolt speed. The reduced bolt speed may increase the probability of deer jumping the string at longer ranges. So in the big picture i chose the 125s. Decent benefits and not too much compromise on bolt speed.
As far as whether your bow will like one brand over another should not really be an issue. At most you may have to adjust your scope when moving between brands but ultimately once the scope is adjusted to any decent quality brand the heads from that brand should group consistently. You are more likely to have issues with the shafts causing grouping issues from one shot to the next. I test every shaft that i intend to hunt with using a designated target broadhead that is identical to my hunting broadhead. Once happy with the performance the target broadhead gets removed and the hunting broadhead goes on and than i take one target shot with the hunting broadhead to confirm zero. That head than stays on that shaft until i kill something with it.