The biggest criticisms (apart from of the general cronyism) are that it's unelected, and also that, as the House of Commons can overrule it, it's somewhat redundant and powerless anyway. Not too long ago I would've shared this viewpoint, but now I've come to realise that both these things are actually good.
It's like the relationship between a writer and an editor..
A writer writes a book. They then send it to an editor who makes some changes and suggestions. Who has ultimate power in this relationship depends upon the circumstances. If the writer is self-publishing, then they're in charge. So they can choose to overrule the opinions of the editor.
"I've listened to your advice, but I disagree with it, so I'm going to publish without your amendments."
Whereas if the writer is working for a larger publisher the editor may have the power.
"We're sorry, but we refuse to publish your book, unless you make these changes."
Ultimately, someone has to have the final veto on the decision. Either way though, whoever has the power, it's still good to employ the services of an editor. Their feedback and opinions are useful. They can take the time to thoroughly inspect the work. They may spot things that you didn't spot when you were toiling away writing it.
The House of Commons is like a person who can self-publish..
They have the final power of veto. Given that they're the elected chamber, then this is how it should be. They should be able to overrule the Lords when push comes to shove.
Again though, that doesn't mean that it isn't useful to have the House of Lords. The back and forth between the Commons and the Lords - like the back and forth between an editor and a writer - provides valuable checks and feedback. They can take the time to debate and inspect legislation. They may spot or foresee things that the Commons didn't see when they were creating it.
If we had an elected House of Lords it would just create confusion over where ultimate power lies. We'd have a constitutional crisis if there was disagreement and some impasse was reached.
So, I've come to the conclusion, that personally, I'd just leave things be.
(As I re-read this back, looking for errors and spelling mistakes, I'm acutely aware of how valuable an editor or proofreader would be.)