Does one style of play have an advantage/disadvantage over the other?
Are today's GMs mostly tactical players or positional players?
What GMs should I follow if I want to be more of a tactical player or positional player?
I don't think one style has an advantage, or at the GM level, there would only be one style; the other would be extinct.
The very definition of a tactical player is Mikhail Tal AKA 'The Wizard of Riga.' Others include Bobby Fischer and Garry Kasparov. Anatoly Karpov and Tigran Petrosian are great examples of positional players.
Fischer himself said that tactics flow from a superior position.
Edit: I'd like to add that any of the top players can find the best move in a given situation. Where positional versus tactical considerations come into play is where there isn't a best move, as such. That is, when there are several reasonable candidate moves. Then some players show a positional tendency while others show a tactical tendency. Petrosian, who is probably the most defensive GM, was more than able to uncork technical savagery if his opponent let him. However, he preferred to tighten the noose instead of looking for a brilliancy.
Tactical playing style has no advantage on positional playing style, and vice-versa.
Although, a single player may have a psychological edge on another player with opposite playing style, in specific situations. In a tournament, for example, if a positional player knows that he's facing a tactical opponent that for some reason needs the full point, may choose a solid system with very few victory chance but no weak points. The tactical player will probably try to force combinations even if the position on the board wouldn't allow such tactics. Then the solid player will only have to defend (supposing he's good at this), and take the full point himself after the opponent's suicide. The same is true also when who needs a full victory is the positional player. He'll try to go for an aggressive play, but he will face a tactical opponent who feels more comfortable in complicated situations, and eventually the positional player will make a blunder and get punished by the opponent.
The key is not the advantage that tactical play has over positional play (or positional over tactical). The key is that if you know that you're facing an opponent with a playing style that's the opposite of yours, you should try to involve him/her in positions he/she doesn't feel comfortable with, while you are. Mikhail Tal was a master at this: his style was so complicated and filled with tactics that when he managed to catch an opponent in his net he had no escape. Petrosian was a master on the other side, playing sober games, choosing super-positional and kinda-drawish systems so that he'd never lose, and win when opponents tried with no hope to break the wall he built.
As World Champ Magnus Carlsen often says "Having preferences means having weaknesses"
In reality there is no such thing as "positional" or "tactical" style. Objectively, it's simply the degree to which the position calls for calculation. This gradation is only necessary because, unlike computers, humans can tire and cannot look 20 moves ahead in an instant. Thus in quiet positions, we use positional understanding (try to improve our position). In sharp positions we focus on calculation because a single misslip usually costs the game.
I have seen an informal distinction between tactical and positional, or put another way between tactical and strategic play.
Tactical play was described as being what you do when you can force the issue. The play can be calculated and the outcome determined. Many lines in game analysis are of this type usually ending with something like "winning a pawn" or any other concrete goal.
Strategic or positional play was described as being what you do when you don't have anything to do. There are no tactical variations that you can use at the moment and so your play must be of the type to create abstract strengths. You increase king safety, or strengthen your hold on the center, or something similar.
Good positional play puts you in a position to find strategic play. Both are important. If you make a positional move while ignoring the strategic considerations it is a worthless move. I once played and game that my opponent analyzed for me afterward, one of his comments for a particular move was "Amazing this move is as good strategically as it is bad tactically" and I had hung the piece simply giving it away.
The other direction is harder to find but ignoring positional play when making a tactical move is the kind where you gain material but make positional compromises that hurt you. One really good example of this is the famous game know as the "Immortal game". Here the winning player had sacrificed a bishop, both rooks, and his queen. Capturing all that material was tactical advantage but the positional considerations were such that the winner was still able to force a win in the end.
There is even some blurring between the two. You might carry out a tactical combination in order to gain a positional advantage.
There is a lot of confusion concerning the terms "tactical", "positional" and "strategic".
First of all, "strategic" and "positional" are not the same!
Positional thinking consists of static short-term considerations concerning the health of your position. I.e. mostly pawn structure and piece placement. Strategy on the other hand means long-term planning. For example you might play an anti-positional move because it is part of a long-term strategy. Positional play requires a feeling for the position, whereas strategic play requires knowledge, logic and systematic considerations.
Now this "feeling for a position"-thingy makes a lot of people open up a dichotomy between the tactical and the positional player, where the tactical player does concrete calculation and the positional player just feels where to put his pieces.
There is enough truth in this dichotomy to make it a very persistent myth. Unfortunately it breaks down if you look at the reality. Being a strong calculator doesn't mean you are a tactical player and a very intuitive approach doesn't turn you into a positional player.
On the contrary, strong positional play is often based on very accurate calculation and strong dynamic play is often based on an intuitive grasp of the position.
Two examples: Positional genius Tigran Petrosian was well known for his exceptional calculation ability. Attacking wizard Mikhail Tal was able to play crazy positions better than anybody because of an incredible feeling for the dynamics of a position (he was regularly outcalculated by players like Kortchnoi).
From my point of view you need intuition for positional and dynamic play and you need systematic thinking for calculation and strategic planning. The most interesting battles often occur if an intuitive player is matched up with a "logician". Sometimes the intuitive player will be an attacking player and the logician will be the strategist (for example Tal-Botvinnik), sometimes it will be the other way round (Karpov-Kasparov). Two players of the same type are more likely to have a very lopsided score (Shirov-Kasparov comes to mind).
This also answers the question (finally…), no style has an advantage over the other. If you really want to dominate somebody, you best have the same style and do everything just a little bit better.