Alrighty, strings changed, tunes jammed, wife annoyed... my work here is done.

Thanks for the compliments on the bass! That is my baby, known to all my friends as Bassby. It even made it on our Christmas card the last two years, haha!
So the TC BQ500 is a great amp, and probably the best value in its class. I also had had the aforementioned MarkBass LM BL250 and sold that awhile back, but still have the TC for now.
I like the 4 band EQ, and it always gives me plenty of clean power. I haven't gigged it hard or anything... my church setting is pretty mild. We have a mediocre setup and no subs, so I run through my own rig and not FOH. We're also pretty small, seating about 200 max pre-rona. We do have a caged drummer, but I don't hafta do anything crazy to blend in. In this setting I don't need any extra drive or grit... but I DO like some.

I'm not a pedal guy. Bass -> instrument cable -> amp -> speaker cable -> cab. Dat's it.
Have you pumped up the gain on your BQ500 for some grit/OD? If so, what do you think about what came out? Did you like it? If you liked it, then awesome!
I, sadly, didn't like it. At. All. For me, this is not a gain stage designed to create pleasant harmonics/overtones/allthestuffagedhorse said. To me it just sounds like when the batteries were dying in my old JVC KaBoom Box but I kept the woofer level cranked to +6 anyway.
I don't really have a whole lot of experience with compressors, but I often left the "Thrust" on just a smidge and I kinda liked it, I think. It also has a bit of an eq circuit in there I believe, but I used it so sparingly I didn't really notice much of a difference. It wasn't something I NEEDED, and I don't miss it since I have been using other amps the last few months. I did NOT like it set anywhere past 10 oclock. Just got squishy and weird after that to me. If you LIKE that feature, realize it's something you'll lose with a Tone Hammer. I think the Ashdown has a compressor though, right?
As for the banana to beefsteak comparison, it is this: you eat a banana as-is. It is simply what a tree produced, and you eat it. To me, the BQ500 takes what it gets from the bass and makes it louder. Yes, you have a 4 band eq, but it doesn't really impart any additional mojo or character of its own. That IS NOT a bad thing! Especially if you have a great sounding bass!
The Tone Hammer/TT800/and I'm hoping the GK Legacy and Ashdown RMII ... are the beefsteaks. You can take that meaty signal, ground and hot from your bass, marinate it with some tasty harmonic content and add rich overtones of pleasant pre-amp clippings, putting out that sear and sizzle that you just can't get with a banana.
Vanilla vs rocky road
Ford vs Ferrari (but not like in the 1960s)
Carrier pigeon vs AlGore's very own internet
Nothing wrong with any of those things, and they all do their task. Heck, vanilla is actually my 2nd fav ice cream, and I have 2 Fords!
From the reading I did and now the experience I've had with the Tone Hammer, there is actually a lot happening with the gain and drive knobs. They are NOT traditional in function like on a tube guitar amp or something. I don't know the parts/math behind what's happening there, but those two knobs alone get me about 85% of the way to where I want to be before even touching the eq. A little searching here on TB and you'll find other people whom have better explained what's going on behind the faceplate of that little wonder. Sadly, Aguilar did NOT write a great manual like Agedhorse, Chef, and I forget other dude... the manual for the TT800 reads like a friendly tone-wizard's textbook, explaining which knob does what and WHY!
Though the Aguilar press department didn't keep up, I feel there are similar levels of elegant tone engineering in the amps of both brands, though their goals and the way they go about them are different.
I'm expecting to be similarly impressed with the GK Legacy, and curious but not overly optimistic about the Ashdown.