I mained dota, then met my brother-in-law who's a plat leaguer. Since then, we've both picked up each others games to play together, and both prefer our own. So it goes. But that interaction has given a lot of insight into the difference between the two games.
League has a big emphasis on counterplay (as you know. ;) ) That's mechanically outskilling your opponent, and making his skills not have full effect. It's great and fun.
Dota's emphasis is more on counter-tactics. You don't lose because you don't have counters (outside of redundant cases like 'I bought armour instead of MR into a full AP team'). You lose because you fail to plan and execute your engagements such that they can't use their skills effectively. This is why CC and mobility are so strong in dota (and so itemizable, so you can invest in better tactical tools), and why there're way more fog of war tools (terrain, cuttable trees, smoke of deceit, nighttime, team ward limit of 4). The goal is to allow you to decide, based on your initiation, how exactly you will cripple the enemy team. Of course, they're trying to do the same thing, and teamfights rarely occur as a surprise to either team. Surprise teamfights tend to be quick and lethal to the surprised one. Normal teamfights often drag out to 15-30 seconds of tactical maneuvering and ccing.
It's definitely fine to prefer league. League has a really fun fighting-game-esque style, where your mechanics and movement are the defining skill-point. Almost all champs have a HERO moment when they land that hook or whatever. It's seriously great.
On the other hand, Dota is fun too. It's a much stronger game strategically, with strategies revolving around map control and variable power spikes at different stages of the game, variable farm allocation based on predicted initiation or counter initiation needs, etc. (Seriously, it's NORMAL in pro games for the carry or mid to leave their lane and let the support farm up an item. That support will end with the lowest CS, but getting him an initiation item is valued more than rushing a better carry item.)
As an example, let's look at BKB: BKB is tactically controlled.
Unlike in league, you CAN'T cleanse out of stuns. So, the first tactical solution to BKB is simply to get the drop on your enemy. Stun or polymorph them before they pop BKB, and burst them. Dota burst is weaker than league's, but with good coordination or stun stacking you can do it.
BKB has a short duration (for Dota teamfights) which gets shorter with every use, and is on a 70ish second CD. So a strategy+tactics solution is to organize ganks on the BKB carrier every 70 seconds, forcing out BKB charges to stay alive, or forcing him to group and farm inefficiently.
Next, you kite it. A BKB lasts less than the normal duration of a fight anyhow. Disengage counters BKB, as it runs out, and then you are effectively an item up on the enemy (BKB stats are terribly inefficient. Like, less than 50% efficient.)
Finally, more than half the skills in the game pierce BKB. It blocks most spammable, low-time-cost cc, and some huge teamfight CC and damage. Heros with no tools vs BKB are somewhat defined by that. There are kiting skills vs a BKB on most teams, even in all random.
Edit: tl;dr: The decision between Dota and League is not one of counters vs counterplay, but one of mechanical vs tactical play.
and 
clearly show why this isn't fun and just unnecessary.
Are some examples.
Because that's not fun mkay?
on a 12(ish?) CD, with a much larger range, but gets disabled if you take hero/hero summoned unit (example would be Tibbers) for 3 seconds.
3-hit procs, but some champs cough 
and you get 
, and it makes it extraordinarily difficult to deal with. The other champs, if I get a proc on me I still feel like I can fight back. When Ekko gets 3 hits on me, I feel like I have already lost the trade and he is running circles around me and I can't do anything to fight back.
Eye learn through hitting my enemies 3 times
