Chops. Laiho is one of the young guys on the metal-scene that really knows how to play. He has all the flashy tricks down and uses them a lot, screaming dive bombs, artificial harmonics, tapping etc. But his biggest strength is that he is freakin' fast. He can probably hang with most of the fastest guys from the 80s. He has alternate picking down perfectly but can also do sweeps a la Malmsteen.
Feeling and melody. Though he is fast and do quite a lot of burning you never feels like he plays without purpose, the solos are going somewhere and you can really feel that Alexi puts his heart into every note.
You can also hear his sense for melody in his songwriting
Dynamics. Laiho knows how to really blend those really heavy death metal type riffs with blistering solos to get a great effect.
Playing in the genre he does, although Children of Bodom are among the lighter bands of their kind, they still are waaay heavier than most people can handle. You don't play Children of Bodom for your mother-in-law. And in the band he plays a more accessable type of metal, Sinergy, he don't get a lot recognation.
Sometime his brutal persona and playing style gets too much. At some point you just can't handle more "fucking fucks" in the lyrics, the sledgehammer riffs and Wylde-esque squeals.
He is certainly very influenced by neo-classical players like Yngwie Malmsteen. The first thing you recognize with Bodom is that the guitar-parts are very classical sounding.
His lead-style is very 80s in it's approach, there is lot of flashy tricks. He especially uses the bar a lot. He also loves doing squeals but don't overuse them, he makes sure they have some impact when he decides to pull them out.
His rhythm is very modern sounding. He either those those fast chugging power-/thrash-metal styled lines or those very heavy kind of death metal type sledgehammer riffs. He has gone from used the former most in the early days to gravitate to the later one more and more today.
He also sometimes plays leads during the verses and choruses. there are a lot guitar-melodies going on under his singing.
Randy Rhoads type Vs. Early on he played Jackson Randy Rhoads models. Somewhere along the way they got lost or stolen and Laiho got an endorsement deal with ESP, which now provides him with guitars that look almost like the Jackson RRs (there are some differences, for example the size of the horns and there is a cutaway on ESPs for better high fret acces).
All his guitars are equipped with Floyd Rose-bridges. Which is a very vital part in his playing style.
For p'ups he goes with EMG-HZ. And he certainly have that very tight "chugging" tone at least I associate with EMG. EMG now have released a signature Alexi Laiho pickup-set.
Children of Bodom where one of the first bands along with Swedish In Flames to have some kind of major breakthrough within the melodic death metal genre and have kind of paved the way for other Scandinavian bands.
All of their six studio efforts are certified at least gold which is really impressive for a metalband these days!
When Alexi Laiho was asked to choose one era in time to experience he said he wished he had been in L.A. throughout the 80s to see the boom with all the great guitarplayers and bands hanging out there during that time.