Should I tag both skills to get the most out of a swift talking gunslinger that I want to start? How important is Science?

Science is as important as lockpick, though it has more dialogue options as well. Science is used to hack terminals which can be, in some cases, used to disengage locks. But i don't see a connection between science and a swift talking gunslinger.

it's very important (it not only determines your skill points but also your ability to hack terminals etc), but sometimes I feel that playing a game is more challenging with not so high science.
Well, I wouldn't tag it if I were to play a swift-talking gunslinger.

I read that Science had dialogue checks too and since I want to be a master talker I wasn't sure if I should focus on it, along with Speech.

Doesn't that fall under intelligence?

You're right, I confused the two.

I play a smooth talking gunslinger with a high speech and barter, but I've never put any points into the Science skill. I plan to create a character who will focus on Science, Medicine, Energy Weapons, Speech and Barter.

How effective are energy weapons vs regular guns?

I love energy weapons. I've always ditched regular guns by the time I leave Novac. Energy weapons have high crits so they're better suited a stealthy character IMO. You can't really run n gun with em until late in the game. Sorry, still drooling over the gauss rifle, my favorite non-dlc weapon.

And you get Meltdown which is the ultimate sniping engery weapons expert's friend. svcks at close range though (not that you'll be in close range much ).

Yes but for a "gunslinger" I would much rather have a higher intelligence since the INT checks are more about saying smart things than correcting people's science.

A swift-talking gunslinging scientist?

Maybe he uses plasma pistols?

Generally speaking Guns are more effective in terms of damage per shot, damage per second, and Guns also have lower cost per shot.

This is probably because the game is heavily biased in favor of the cowboy/western theme, so energy weapons are nerfed.

The GRA energy weapons are better, and their are some other exceptions like the Holo Rifle from Dead Money, but I'd take an Anti Material Rifle and a silenced 12.7mm pistol or SMG over energy weapons, and a scoped .308 hunting rifle for anything I don't want to waste a .50MG round on.

At best, energy weapons will at give you the same combat performance to their guns counterparts, but at a much higher ammo cost. Quite often, however, their performance is inferior and their cost to operate (i.e. ammo) is higher than comparable guns.

It's sad because in the game lore everyone says energy is great, to be feared, blah blah blah, but it ain't so. At least not in New Vegas. In this game, guns rule.

So Energy Weapons are nerfed? I wanted to max it along with Guns.

There's nothing stopping you from doing so, except yourself. IMO EWs are useful and rather powerful(atleast with the Plasma Defender the End game was a cake walk for me) but ammo is scarce until you find good merchants that sell EW ammo(Van Graffs for example).

Plus you have to decide early on that you're going to specialize in EWs otherwise it'll take a lot of caps and time to compensate.

Nipton, REPCONN HQ, REPCONN Test Site, Durable Dan's Sacked Caravan. By the time you're level 8/9 and hitting Freeside/The Strip you have a full arsenal of EW at your disposal. TBH, I've always found the Van Graffs to be widely over-rated until you blow up/butcher them and jack their stuff.

The fiends are also a near endless supply of MF and EK cells. Also, it's much easier to recycle EW ammo than Gun ammo and you can convert between types (except for Flamer Fuel). End game I have over 3.5k Energy cells and over 3k MF cells.

Unlike F3, you can be packing serious EW heat by early to mid-game in FNV.

Moreover,

What's the difference between EF and MK?

They're just different ammo types for energy weapons. Just like all the guns don't use the same ammo, all the energy weapons don't use the same ammo either.

I go with Guns, Medicine, Repair.

I used to insert sneak instead of Medicine, but I don't enjoy Sniping at all anymore. Running-and-gunning is what I enjoy doing now.

You should tag both because, science makes you better at creating drugs and some meds at a campfire and hacking computers. The speech skill is the common skill you will have to use when convincing someone.

Is it better to have a high level Science or Lockpicking?

with science you can craft stuff and access some computers which usually add to the story, as well as sometimes unlocking doors. Lockpick opens doors and containers that have loot. It's all preference. With all the DLCs you should be able to get them both to 100 with time.

I can't tag both Science and Speech because then i'll have only one more skill to tag for Guns and Energy Weapons. I want to get both of those to 100 and me a master gunslinger.