Personally i think every player regardless of style they choose should study up on tactics. I also believe you should continue to develop along ur natural strengths and build on that foundation. If u try and play whats not natural i think u get into more issues, but thats my opinion anyway. Karpov plays more positional for eg but still knows his tactics but he isnt overly aggressive, where Kasparov is alot more tactical minded and aggressive, but still knows how to play positional chess too. But they always seem to play to there natural styes and build around that....
Which approach should I take in improving my game?
Unless you can force all your games to be closed, you'll always be in a bad spot. If I knew I had a weakness in a particular style of play, I would try to improve that area.
if you want to learn your tactics you could join this group:
http://www.chess.com/groups/home/tactics-improvers
I have a new puzzle up each day
I have noticed a trend on my previous games against friends (away from the internet, I'm new to online chess) that I am far stronger in closed, defensive games than in open and attacking ones. I find that I am able to hold my own against quite good opponents in closed games, but I often struggle to beat quite poor players in open games.
My question is as follows: Given that I have limited time to study, should I focus on looking at games by attacking players and concentrate on tactics and improving that side of my game, or stick with what I am best at (I think there is only so far I could approve my calculating ability) and look at games by those that specialised in closed defensive games and positional play, which I find naturally easier?