I love my HotPlate. I've never used a Weber but I've heard great things about them too. I'm not sure of the options available on a Weber as far as knobs and switches, but the HotPlate has deep and bright switches that you can turn on/off to compensate for the loss of those frequencies based on the amount of attenuation you use. Plus the HotPlate has 2 outputs (you can drive 2 cabs from 1 HotPlate) and a line output for post-amp effect placement, built-in noise reduction, a dummy load setting (basically a speaker defeat) and variable attenuation below -16 dB.
One word of advice though about attenuators, and that's to keep your expectations realistic. Yes they can bring a raging tube monster down to bedroom levels, but there's a cost as far as tone. The more you attenuate, the more your tone is affected. By the time you attenuate enough to play at midnight in your bedroom without waking the sleeping baby in the next room, your tone doesn't really resemble what you're used to hearing.
But to shave off -4 dB, -8 dB or even -12 dB, it'll do a great job and you'll barely notice the difference except for a few things: 1) Your speakers provide a dynamic or variable load to your output transformer. An attenuator is a static load, so it doesn't quite react to your playing like an unattenuated speaker does, and 2) your speakers add a little bit of breakup to your overall tone when you really get them moving. when you play at quieter volumes, you lose a lot of that speaker breakup. Not a huge deal but you might notice it. 3) one other thing is that while the attenuator itself isn't bad for your tubes, having your amp cranked all the time (as opposed to however often you crank it up currently) will shorten the life of your power tubes.
But all that aside, I still HIGHLY recommend getting an attenuator anyways. These detriments to your tone are small potatoes compared to the ability to really cook the power section of a tube amp. Having the master volume low and not really pushing your power tubes sounds so sterile compared to the dynamic range and punch available by really pushing the power section.
My 80-watt 2x12 tube amp would be nearly useless to me without my HotPlate since I play entirely in my basement of my house. I don't gig, but if I did it would still be a huge benefit for the ability to control stage volume. It's still loud when attenuated by -12 dB but it really takes the edge off of the volume and makes it tolerable to be next to while playing, and it tames it enough to make it easier to mic without clipping my mic preamps.
So whether you go Weber or THD, I don't think either will let you down. The THD has more options and I can personally vouch for their excellent build quality and great tone. But the Weber has price on its side. It's too bad that so few places carry them so doing a demo or side-by-side comparison will be difficult. See if you can buy from someplace with a leniant return policy and give them both a try.
Good luck!