I have voice chat permanently muted when playing Dota 2. People can write "mia" with no effort (or use the chat wheel, for that matter), and I honestly dont need to be told a myriad of colorful names in a variety of dialects and languages every day of the week, thank you very much. I gotta admit, I do miss the pause function tough.
Now, about "hard counters". To be honest, there are situations in both games where you can "counterpick" the Enemy hero, at least to a degree. In the end, it still comes down to your eprsonal skill and teamplay tough. As Putnam said, even if the Enemy plays a hero/champion you have problems dealing with, if you have a competent team they will help out, or swap lanes. Granted, in LoL Lane-Swaps seem to be pretty rare, but that's what the junglers for. To bust your ass out of jail when things get rough.
Not just judging from the heroes themselves, but also item and mechanic-wise, the games arent really comaprable anyway. First of all there's the courier, so you can deliver shop items to the lane directly without leaving. Then you have pretty hardcore Item choices like Refresher Orb, which allows you to reset all Cooldowns every few minutes, or Dagon, a portable Laser that deals enough Damage to almost one-shot squishy heroes. (800 Damage on Level 5, if I remember correctly, with a 20 sec CD) Not to talk about Blink Dagger, which allows you to teleport short distances and thus a favored choice by almost all initiators. I cant see any of those be integrated into LoL without completely tilting the balance.
A mate of mine once said that LoL's balancing works with tweaking, nerfing, and buffing. While Dota's balances itself by countering op with even more op. And I find that strangely adequate. In many ways, especially in early game, I find LoL's gameplay almost soothingly relaxing, compared to some of the Level 1 Doom Rays, 5 man Roshans (who puts the entire Team 2-4 level up from the get go) and 5 second stuns as a normal abilty, all the while a russian calls you a bitch with voicechat over in Dota.
The two are really further apart than most people think. I think the only thing both share without qualifiers, is the horrible community.