I'm completely in agreement with the idea that English affairs should be determined by parliamentarians elected in England. Why should Scottish MPs be able to vote on laws relating to education or health in England, when these areas are fully devolved to Scotland? However, the way to achieve this would be to create an English Parliament and an English Government separate from the UK institutions, not the EVEL plan that the Tories have put in place.
As Lallands Peat Worrier has argued, EVEL really doesn't implement English Votes for English Laws but English Vetoes against but not for English Laws. This sounds rather innocent, but EVEL has evil consequences for all MPs representing non-English seats and any parties that rely on them.
The purpose is to give the Tories a perpetual veto at Westminster. The consequences might be minor during this parliament. However, as Iain Macwhirter has pointed out, EVEL will suddenly become important once a (possibly Labour-led) government relies on non-English MPs to pass its legislation: "It would leave UK Labour ministers for health, education and justice unable to implement the policies on which the government was elected. How could any prime minister pretend to govern when he or she can’t implement their manifesto pledges over 85 per cent of the UK population?"
A useful way to think about it might be so say that we currently have Tory governments in both England and the UK so there are no conflicts; however, if after 2020 we have a Tory government in England but any other government in the UK, EVEL will suddenly spring into action. (Holyrood politics was also a bit boring while Labour was in charge both there and in the UK and only really got interesting after the SNP got into government.)
It is now unrealistic for MPs from Scotland, Wales and Northern Ireland to reach the top. Positions such as Prime Minister, Chancellor of the Exchequer, the Secretaries of State for Health and Education and the Home Secretary will now require the holder to represent an English seat, as pointed out by Wings over Scotland. The problem is that most politicians move up through government by advancing to a more important post from time to time, so it becomes almost impossible to create a reasonable career path if you are restricted to military and foreign affairs.
It might also shut non-English MPs out of a lot of the committees (where a lot of the real law-making happens) -- see for instance this story about Tommy Sheppard's seat in the fracking regulations committee. This is all a bit odd because English MPs don't seem to have been removed from the Scottish Affairs Committee, which has plenty of members not representing Scottish seats.
Of course, there's also the worry that EVEL will be extended in the future. Currently it's just implemented through a Commons standing order, which a future government can easily change. It'll be interesting to see whether the current government after a couple of years tries to make it much harder to change by putting it into law once the dust has settled.
It will also be interesting whether the Tories will try to lump together legislation to make it impossible for Scots to block. For instance, English fox hunting legislation is now subject to an English veto, but Scots can still take part in blocking it in the final stage if it's a close vote (i.e., if a lot of Tories rebel). Might the Tories add a Scottish sweetener to the bill to make it unattractive for Scottish MPs to do this?
It's also worth bearing in mind that EVEL isn't a symmetrical response to Scottish devolution. The way to determine whether something is devolved to Holyrood isn't to ask whether it only affects Scotland but to check a long list of reserved matters. For instance, broadcasting is reserved to Westminster, so Holyrood cannot simply create a new Scottish TV channel; on the other hand agriculture is reserved, so Westminster cannot pass a UK-wide law in this area without Holyrood's consent. It would have been straight-forward enough to attach a similar list of reserved matters to the EVEL standing order (which is surely what they would have done if they had set up an English Parliament), but instead it's been left to the discretion of the Speaker.
It's hard not to get the impression that the Tories have made the first version of EVEL deliberately vague so that nobody gets too bothered about it yet, and by the time people really realise what it was all about, it will already have been part of the UK's uncodified constitution for years. That's EVEL.