Insulated Mittens or Gloves for alpine mountaineering?

I am debating which one is better to use for a mountaineering trip. All I heard is that mitten is warmer but limit use with hand/finger on activities like climbing, rope, etc. For gloves, it is not warm as mittens but is easier to handle the rope, grab something to climb, etc. Can anyone give me advice which is better? Right now I am looking at Outdoor Research Alti Mittens and Alti Gloves.

It depends where/when you are going. Probably both.

For anywhere high where it could be cold, you really need a big fat "oh shit" mitten so you don't get frostbite even if conditions are worse than you expect. You'll probably want to use gloves most of the time unless it's super cold.

I usually bring a light softshell glove for protection during self-arrest and warmth while plunging an axe, maybe a thicker glove for colder starts or activity during cold weather, and a back-up pair of thick mitts in the bottom of the pack.

I have the Alti Mitten and use them frequently in winter. My glove system usually involves a thinner glove (Rab Alpine Glove at the moment) that dries fast and provides good dexterity. I remove the insulated liners from the Alti Mitts and use the insulated shell over my thinner gloves. My hands stay warm, dry, and when I need to remove the mitts I still have a glove on my hand for technical climbing/anchor management or whatever.   

It's impossible to make recommendations without knowing where/what you plan to climb.

What Nick said.  “Mountaineering Trip” is pretty vague for accurate or valuable advice.  

However as others stated above, a dexterous glove for technical combined with an outer mitten for warmth (emphasis on which part depending on the climb/season/location, etc) will cover about 80% of your needs

Gloves are worth their weight in gold. I  carry 2 pairs of gloves and a pair of mittens.  

Yep, have both in your kit and bring what is needed for each specific situation.

Again, it all boils down to what "alpine mountaineering" means to you.  If you're going alpine climbing, ie: technical roped ascent on grades that include alpine ice (AI), water ice (WI), alpine rock or mixed routes (M-) you will want several pairs of thin, but insulated gloves for active climbing.  For emergencies & cold belays, you will want the warmest, most dexterous mitten you can find.  That's next-near impossible as every mitten I've ever worn/seen has next to no dexterity whatsoever, however, there's nothing like a fat pair of mittens when your fingers go numb.  Please don't take this the wrong way, but if you're asking this question, I doubt you're ready for the severity of an alpine environment.