I hesitate to make sweeping statements about any large group of people under a banner that holds places for many people of differing relationships with religion and magikal practices. I doubt that there is more power or that it comes more quickly. I have had minor experiences with folks from left hand paths and for the most part they are people just like everyone else. Their magik is neither stronger nor harder to defeat than any other magik.
I know very little of true Tantra but have never considered it part of the left hand path.
Oh, most definitely- whatever definition you manage to use for a path with whichever many caveats, you'll always find people who can claim the path as their own but not conform to your definition

Generalisations, I find, are fine enough for kicking off understanding and aren't harmful as such.
I didn't mean to say that Left Hand paths offer
more power, just that it usually ends up giving results faster.
Tantra is a Left Hand path to the Divine because it doesn't ask you to detach yourself from attachments or abstain (contrast this with the Right Hand form of worship,
Sadhna where you're encouraged to leave behind worldly attachments in pursuit of God)...rather, it proclaims, "The very vehicle which takes you to deepest depths of the Netherworld will be your Chariot to the highest Heavens"
In practice, it also has a very involved mythology surrounding Shakti and Shiva, some of which aren't acknolwedged by mainstream Bramhanical Hinduism. Indeed, Tantra is said to be the under the sole purview of Shiva and Shakti.
Also, while we're on the topic of practical Tantra, it plays fast and loose with earthbound spirits, specifically people who have passed in untimely, violent ways.
I've never studied Tantra from the inside, but from the outside looking in, it seems fairly easy to divorce the spiritual side of Tantra from its practical magical/occult aspects.
As it stands, very few people get into it these days for the spirituality- and as you could guess far better than I could...the results aren't very pretty when you set out trying to control spirits without an underlying spiritual/moral/ethical safety net to rely on.