I'm getting back into magic too, but I took my break back in Mirrodin and mostly play Limited, so take everything I say with a grain of salt.

There's a range of types of "competitive," very casual all the way to professional, in different formats (what cards you are and aren't allowed to play). So...

If you want to be "competitive" at a high(ish) level, you have to know some of the common archetypes for the format. You're playing with new cards, your format is probably Standard, (goldfish) [http://www.mtggoldfish.com/metagame/standard#paper]is a good site that keeps track of the metagame.

Briefly looking through that, the event deck doesn't seem to have too many staples, but you're on the road to a (G/R Dragons) [http://www.mtggoldfish.com/metagame/standard#paper] with the regent. Many people would say that looking for budget versions of this or similar decks would be a good place to get started. Search green red budget standard and you'll be overwhelmed with options, suggestions and advice on building one of your own.

That said, if you're sticking with these event decks for now (which I think is great! I have yet to buy singles personally, my constructed deck is made up of the few cards I keep from playing limited so it mostly loses but I'm becoming a better player and learning what I might want to invest in if i start taking constructed more seriously).

So the very little advice I have for you to combine these decks: 1: you want consistency in the main deck. So choose some of the spells that seem to be doing the most for you and double up on those in lieu of the duds. 2: your sideboard, on the other hand, needs to be versatile: include cards that are good if you're up against control or need to respond to different threats. At the very least, include cards that become good against different colors. Sideboards are vital for matches, and deciding what to switch about your deck between games in a match is like extra credit in the learning process! 3: the mana curve is important, which the event deck actually seems to do a good job of. I always judge success against some opponents as "was I able to complete a good turn, regardless of how much better a turn my opponent might have made?" 4: EVERY rule in magic has an exception 5: except this one, Have Fun!